Advances in Operator TheoryAdvances in Operator Theory
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Wed, 21 Mar 2018 12:17:16 +0100FeedCreatorAdvances in Operator Theory
http://www.aot-math.org/
Feed provided by Advances in Operator Theory. Click to visit.Different type of fixed point theorem for multivalued mappings
http://www.aot-math.org/article_48945_6058.html
In this paper by using the measure of noncompactness concept, we present new fixed point theorems for multivalued maps. In further we introduce a new class of mappings which are general than Meir--Keeler mappings. Finally, we use these results to investigate the existence of weak solutions to an Evolution differential inclusion with lack of compactness.Sat, 31 Mar 2018 19:30:00 +0100Linear preservers of two-sided right matrix majorization on $\mathbb{R}_{n}$
http://www.aot-math.org/article_53654_0.html
A nonnegative real matrix $Rin textbf{M}_{n,m}$ with the property that all its row sums are one is said to be row stochastic. For $x, y in mathbb{R}_{n}$, we say $x$ is right matrix majorized by $y$ (denoted by $xprec_{r} y$) if there exists an $n$-by-$n$ row stochastic matrix $R$ such that $x=yR$. The relation $sim_{r}$ on $mathbb{R}_{n}$ is defined as follows. $xsim_{r}y$ if and only if $ xprec_{r} yprec_{r} x$. In the present paper, we characterize the linear preservers of $sim_{r}$ on $mathbb{R}_{n}$, and answer the question raised by F. Khalooei [Wavelet Linear Algebra textbf{1} (2014), no. 1, 43--50].Sat, 02 Dec 2017 20:30:00 +0100Singular Riesz measures on symmetric cones
http://www.aot-math.org/article_50058_6058.html
‎A fondamental theorem due to Gindikin says that the‎ ‎generalized power $Delta_{s}(-theta^{-1})$ defined on a symmetric‎ ‎cone is the Laplace transform of a positive measure $R_{s}$ if and ‎only if $s$ is in a given subset $Xi$ of $Bbb{R}^{r}$‎, ‎where $r$‎ ‎is the rank of the cone‎. ‎When $s$ is in a well defined part of‎ ‎$Xi$‎, ‎the measure $R_{s}$ is absolutely continuous with respect to‎ ‎Lebesgue measure and has a known expression‎. ‎For the other elements‎ ‎$s$ of $Xi$‎, ‎the measure $R_{s}$ is concentrated on the boundary of‎ ‎the cone and it has never been explicitly determined‎. ‎The aim of the‎ ‎present paper is to give an explicit description of the measure‎ ‎$R_{s}$ for all $s$ in $Xi$‎. ‎The work is motivated by the‎ ‎importance of these measures in probability theory and in statistics‎ ‎since they represent a generalization of the class of measures‎ ‎generating the famous Wishart probability distributions‎.Sat, 31 Mar 2018 19:30:00 +0100Pompeiu-Čebyšev type inequalities for selfadjoint operators in Hilbert spaces
http://www.aot-math.org/article_54087_0.html
In this work, generalization of some inequalities for continuous h-synchronous (h-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved. .Fri, 15 Dec 2017 20:30:00 +0100Cover topologies, subspaces, and quotients for some spaces of vector-valued functions
http://www.aot-math.org/article_51020_6058.html
‎Let $X$ be a completely regular Hausdorff space‎, ‎and let $mathcal{D}$ be a‎ ‎cover of $X$ by $C_{b}$-embedded sets‎. ‎Let $pi‎ :‎mathcal{E}$ $rightarrow X$‎ ‎be a bundle of Banach spaces (algebras)‎, ‎and let $Gamma(pi)$ be the‎ ‎section space of the bundle $pi‎ .‎$ Denote by $Gamma _{b}(pi‎,‎mathcal{D})$‎ ‎the subspace of $Gamma (pi )$ consisting of sections which are bounded on‎ ‎each $Din mathcal{D}$. We construct a bundle $rho ^{prime }:mathcal{F}‎^{prime}rightarrow beta X$ such that $Gamma _{b}(pi‎ ,‎mathcal{D}) ‎$ is topologically and algebraically isomorphic to $Gamma(rho^prime‎‎)‎$, ‎and use this to study the subspaces (ideals) and quotients resulting‎ ‎from endowing $Gamma _{b}(pi‎,‎mathcal{D})$ with the cover topology‎ ‎determined by $mathcal{D}$‎.Sat, 31 Mar 2018 19:30:00 +0100Perturbation of minimum attaining operators
http://www.aot-math.org/article_54270_0.html
We prove that the minimum attaining property of a bounded linear operator on a Hilbert space $H$ whose minimum modulus lies in the discrete spectrum, is stable under small compact perturbations. We also observe that given a bounded operator with strictly positive essential minimum modulus, the set of compact perturbations which fail to produce a minimum attaining operator is smaller than a nowhere dense set. In fact it is a porous set in the ideal of all compact operators on $H$. Further, we try to extend these stability results to perturbations by all bounded linear operators with small norm and obtain subsequent results.Tue, 19 Dec 2017 20:30:00 +0100Integral representations and asymptotic behaviour of a Mittag-Leffler type function of two variables
http://www.aot-math.org/article_51110_6058.html
Integral representations play a prominent role in the analysis of entire functions. The representations of generalized Mittag-Leffler type functions and their asymptotics have been (and still are) investigated by plenty of authors in various conditions and cases.The present paper explores the integral representations of a special function extending to two variables the two-parametric Mittag-Leffler type function. Integral representations of this functions within different variation ranges of its arguments for certain values of the parameters are thus obtained. Asymptotic expansion formulas and asymptotic properties of this function are also established for large values of the variables. This yields corresponding theorems providing integral representations as well as expansion formulas.Sat, 31 Mar 2018 19:30:00 +0100Besicovitch almost automorphic solutions of nonautonomous differential equations of first order
http://www.aot-math.org/article_54492_0.html
The main purpose of this paper is to analyze the existence and uniqueness of Besicovitch almost automorphic solutions and weighted Besicovitch pseudo-almost automorphic solutions of nonautonomous differential equations of first order. We provide an interesting application of our abstract theoretical results.Thu, 28 Dec 2017 20:30:00 +0100Operator algebras associated to modules over an integral domain
http://www.aot-math.org/article_51119_6058.html
We use the Fock semicrossed product to define an operator algebra associated to a module over an integral domain. We consider the $C^*$-envelope of the semicrossed product, and then consider properties of these algebras as models for studying general semicrossed products.Sat, 31 Mar 2018 19:30:00 +0100A Kakutani-Mackey-like theorem
http://www.aot-math.org/article_56029_0.html
We give a partial extension of a Kakutani-Mackey theorem for quasi-complemented vector spaces. This can be applied in the representation theory of certain complemented (non-normed) topological algebras. The existence of continuous linear maps, in the context of quasi-complemented vector spaces, is a very important issue in their study. Relative to this, we prove that every Hausdorff quasi-complemented locally convex space has continuous linear maps, under which a certain quasi-complemented locally convex space, turns to be pre-Hilbert.Mon, 22 Jan 2018 20:30:00 +0100On the truncated two-dimensional moment problem
http://www.aot-math.org/article_51181_6058.html
We study the truncated two-dimensional moment problem (with rectangular data) to find a non-negative measure $mu(delta)$, $deltainmathfrak{B}(mathbb{R}^2)$, such that $int_{mathbb{R}^2} x_1^m x_2^n dmu = s_{m,n}$, $0leq mleq M,quad 0leq nleq N$, where ${ s_{m,n} }_{0leq mleq M, 0leq nleq N}$ is a prescribed sequence of real numbers; $M,Ninmathbb{Z}_+$. For the cases $M=N=1$ and $M=1, N=2$ explicit numerical necessary and sufficient conditions for the solvability of the moment problem are given. In the cases $M=N=2$; $M=2, N=3$; $M=3, N=2$; $M=3, N=3$ some explicit numerical sufficient conditions for the solvability are obtained. In all the cases some solutions (not necessarily atomic) of the moment problem can be constructed.Sat, 31 Mar 2018 19:30:00 +0100$T1$ theorem for inhomogeneous Triebel--Lizorkin and Besov spaces on RD-spaces and its application
http://www.aot-math.org/article_57072_0.html
Using Calder'{o}n's reproducing formulas and almost orthogonal estimates, the $T1$ theorem for the inhomogeneous Triebel--Lizorkin and Besov spaces on RD-spaces is obtained. As an application, new characterizations for these spaces with ``half" the usual conditions of the approximate to the identity are presented.Sat, 27 Jan 2018 20:30:00 +0100Compactness of a class of radial operators on weighted Bergman spaces
http://www.aot-math.org/article_51302_6058.html
In this paper, we study some connection between the compactness of radial operators and the boundary behavior of the corresponding Berezin transform on weighted Bergman spaces. More precisely, we prove that, under some mild condition, the vanishing of the Berezin transform on the unit circle is equivalent to the compactness of a class of radial operators on weighted Bergman spaces. Moreover, we also study the radial essential commutant of the Toeplitz operator $T_z$.Sat, 31 Mar 2018 19:30:00 +0100Fixed points of a class of unitary operators
http://www.aot-math.org/article_57403_0.html
In this paper, we consider a class of unitary operators defined on the Bergman space of the right half plane and characterize the fixed points of these unitary operators. We also discuss certain intertwining properties of these operators. Applications of these results are also obtained.Sun, 04 Feb 2018 20:30:00 +0100Extensions of theory of regular and weak regular splittings to singular matrices
http://www.aot-math.org/article_51467_6058.html
Matrix splittings are useful in finding a solution of linear systems of equations, iteratively. In this note, we present some more convergence and comparison results for recently introduced matrix splittings called index-proper regular and index-proper weak regular splittings. We then apply to theory of double index-proper splittings.Sat, 31 Mar 2018 19:30:00 +0100Well-posedness issues for a class of coupled nonlinear Schr"odinger equations with ...
http://www.aot-math.org/article_57444_0.html
The initial value problem for some coupled nonlinear Schrodinger equations in two space dimensions with exponential growth is investigated. In the defocusing case, global well-posedness and scattering are obtained. In the focusing sign, global and non global existence of solutions are discussed via potential well- method.Tue, 06 Feb 2018 20:30:00 +0100On linear maps preserving certain pseudospectrum and condition spectrum subsets
http://www.aot-math.org/article_51460_6058.html
We define two new types of spectrum, called the $varepsilon$-left (or right) pseudospectrum and the $varepsilon$-left (or right) condition spectrum, of an element $a$ in a complex unital Banach algebra $A$. We prove some basic properties among them the property that the $varepsilon$-left (or right) condition spectrum is a particular case of Ransford spectrum. We study also the linear preserver problem for our defined functions and we establish the following: (1) Let $A$ and $B$ be complex unital Banach algebras and $varepsilon>0$. Let $phi : Alongrightarrow B $ be an $varepsilon$-left (or right) pseudospectrum preserving onto linear map. Then $phi$ preserves certain standart spectral functions.(2) Let $A$ and $B$ be complex unital Banach algebras and $0< varepsilon<1$. Let $phi : Alongrightarrow B $ be unital linear map. Then(a) If $phi $ is $varepsilon$-almost multiplicative map, then $sigma^{l}(phi(a))subseteq sigma^{l}_varepsilon(a)$ and $sigma^{r}(phi(a))subseteq sigma^{r}_varepsilon(a)$, for all $a in A$.(b) If $phi$ is an $varepsilon$-left (or right) condition spectrum preserving, then (i) if $A$ is semi-simple, then $phi$ is injective; (ii) if B is spectrally normed, then $phi$ is continuous.Sat, 31 Mar 2018 19:30:00 +0100Closedness and invertibility for the sum of two closed operators
http://www.aot-math.org/article_57481_0.html
We show a Kalton--Weis type theorem for the general case of non-commuting operators. More precisely, we consider sums of two possibly non-commuting linear operators defined in a Banach space such that one of the operators admits a bounded $H^infty$-calculus, the resolvent of the other one satisfies some weaker boundedness condition and the commutator of their resolvents has certain decay behavior with respect to the spectral parameters. Under this consideration, we show that the sum is closed and that after a sufficiently large positive shift it becomes invertible, and moreover sectorial. As an application we recover a classical result on the existence, uniqueness and maximal $L^{p}$-regularity for solutions of the abstract linear non-autonomous parabolic problem.Wed, 07 Feb 2018 20:30:00 +0100Certain geometric structures of $\Lambda$-sequence spaces
http://www.aot-math.org/article_53412_6058.html
The $Lambda$-sequence spaces $Lambda_p$ for $1< pleqinfty$ and their generalized forms $Lambda_{hat{p}}$ for $1<hat{p}<infty$, $hat{p}=(p_n)$, $nin mathbb{N}_0$ are introduced. The James constants and strong $n$-th James constants of $Lambda_p$ for $1<pleqinfty$ are determined. It is proved that the generalized $Lambda$-sequence space $Lambda_{hat{p}}$ is a closed subspace of the Nakano sequence space $l_{hat{p}}(mathbb{R}^{n+1})$ of finite dimensional Euclidean space $mathbb{R}^{n+1}$, $nin mathbb{N}_0$. Hence it follows that sequence spaces $Lambda_p$ and $Lambda_{hat{p}}$ possess the uniform Opial property, $(beta)$-property of Rolewicz, and weak uniform normal structure. Moreover, it is established that $Lambda_{hat{p}}$ possesses the coordinate wise uniform Kadec--Klee property. Further, necessary and sufficient condition for element $xin S(Lambda_{hat{p}})$ to be an extreme point of $B(Lambda_{hat{p}})$ are derived. Finally, estimation of von Neumann-Jordan and James constants of two dimensional $Lambda$-sequence space $Lambda_2^{(2)}$ are carried out. Upper bound for the Hausdorff matrix operator norm on the non-absolute type $Lambda$-sequence spaces is also obtained.Sat, 31 Mar 2018 19:30:00 +0100Parallel iterative methods for solving the common null point problem in Banach spaces
http://www.aot-math.org/article_57735_0.html
We consider the common null point problem in Banach spaces. Then, using the hybrid projection method and the $varepsilon $- enlargement of maximal monotone operators, we prove two strong convergence theorems for finding a solution of this problem.Fri, 16 Feb 2018 20:30:00 +0100Complex isosymmetric operators
http://www.aot-math.org/article_57759_0.html
‎In this paper‎, ‎we introduce complex isosymmetric and $(m,n,C)$-isosymmetric operators on a Hilbert space $mathcal H$ and study properties of such operators‎. ‎In particular‎, ‎we prove that if $T in {mathcal B}(mathcal H)$ is an $(m,n,C)$-isosymmetric operator and $N$ is a $k$-nilpotent operator such that $T$ and $N$ are $C$-doubly commuting‎, ‎then $T‎ + ‎N$ is an $(m+2k-2‎, ‎n+2k-1,C)$-isosymmetric operator‎. ‎Moreover‎, ‎we show that if $T$ is $(m,n,C)$-isosymmetric and if $S$ is $(m',D)$-isometric and $n'$-complex symmetric with a conjugation $D$‎, ‎then $T otimes S$ is $(m+m'-1,n+n'-1,C otimes D)$-isosymmetric‎.Fri, 16 Feb 2018 20:30:00 +0100Variant versions of the Lewent type determinantal inequality
http://www.aot-math.org/article_58027_0.html
‎In this paper‎, ‎we present a refinement of the Lewent determinantal inequality and then‎, ‎we show that the following inequality holds‎ ‎begin{align*}‎ ‎ &detfrac{I_{mathcal{H}}+A_1}{I_{mathcal{H}}-A_1}+detfrac{I_{mathcal{H}}+A_n}{I_{mathcal{H}}-A_n}-sum_{j=1}^nlambda_j detleft(frac{I_{mathcal{H}}+A_j}{I_{mathcal{H}}-A_j}right)\‎ ‎ & ge detleft[left(frac{I_{mathcal{H}}+A_1}{I_{mathcal{H}}-A_1}right)left(frac{I_{mathcal{H}}+A_n}{I_{mathcal{H}}-A_n}right)prod_{j=1}^n left(frac{I_{mathcal{H}}+A_j}{I_{mathcal{H}}-A_j}right)^{-lambda_j}right],‎, ‎end{align*}‎ ‎where $A_jinmathbb{B}(mathcal{H})$‎, ‎$0le A_j < I_mathcal{H}$‎, ‎$A_j's$ are trace class operators and $A_1 le A_j le A_n~(j=1,cdots,n)$ and $sum_{j=1}^nlambda_j=1,‎~ ‎lambda_j ge 0‎~ ‎(j=1,cdots,n)$‎. In addition‎, ‎we present some new versions of the Lewent type determinantal inequality‎.Sat, 24 Feb 2018 20:30:00 +0100wUR modulus and normal structure in Banach spaces
http://www.aot-math.org/article_58068_0.html
‎Let $X$ be a Banach space‎. ‎In this paper‎, ‎we study the properties of wUR modulus of $X$‎, ‎$delta_X(varepsilon‎, ‎f),$ where $0 le varepsilon le 2$ and $f in S(X^*),$ and the relationship between the values of wUR modulus and reflexivity‎, ‎uniform non-squareness and normal structure respectively‎. ‎Among other results‎, ‎we proved that if $ delta_X(1‎, ‎f)> 0$ for any $fin S(X^*),$ then $X$ has weak normal structure‎.Mon, 26 Feb 2018 20:30:00 +0100The Matrix power means and interpolations
http://www.aot-math.org/article_58111_0.html
‎It is well-known that the Heron mean is a linear interpolation between the arithmetic and the geometric means while the matrix power mean $P_t(A,B):= A^{1/2}left(frac{I+(A^{-1/2}BA^{-1/2})^t}{2}right)^{1/t}A^{1/2}$ interpolates between the harmonic‎, ‎the geometric‎, ‎and the arithmetic means‎. ‎In this article‎, ‎we establish several comparisons between the matrix power mean‎, ‎the Heron mean and the Heinz mean‎. ‎Therefore‎, ‎we have a deeper understanding about the distribution of these matrix means‎.Tue, 27 Feb 2018 20:30:00 +0100$C^*$-algebra distance filters
http://www.aot-math.org/article_58258_0.html
‎We use non-symmetric distances to give a self-contained account of $C^*$-algebra filters and their corresponding compact projections‎, ‎simultaneously simplifying and extending their general theory‎. Sat, 03 Mar 2018 20:30:00 +0100On Neugebauer's covering theorem
http://www.aot-math.org/article_58259_0.html
We present a new proof of a covering theorem of C‎. ‎J‎. ‎Neugebauer‎, ‎stated‎ ‎in a slightly more general form than the original version; we also give an application to restricted weak‎ ‎type (1,1) inequalities for the uncentered maximal operator‎.Sat, 03 Mar 2018 20:30:00 +0100The existence of hyper-invariant subspaces for weighted Shift operators
http://www.aot-math.org/article_58113_0.html
‎We introduce some classes of Banach spaces for which the hyperinvariant subspace problem for the‎ ‎shift operator has positive answer‎. ‎Moreover‎, ‎we provide sufficient conditions on weights which ensure that certain subspaces of $ell^2_{{beta}}(mathbb{Z})$ are closed under convolution‎. ‎Finally we consider some cases of weighted spaces for which the problem remains open‎.Sat, 03 Mar 2018 20:30:00 +0100Orthogonality of bounded linear operators on complex Banach spaces
http://www.aot-math.org/article_58482_0.html
‎We study Birkhoff-James orthogonality of compact linear operators on complex reflexive Banach spaces and obtain its characterization‎. ‎By means of introducing new definitions‎, ‎we illustrate that it is possible in the complex case‎, ‎to develop a study of orthogonality of compact linear operators‎, ‎analogous to the real case‎. ‎Furthermore‎, ‎earlier operator theoretic characterizations of Birkhoff-James orthogonality in the real case‎, ‎can be obtained as simple corollaries to our present study‎. ‎In fact‎, ‎we obtain more than one equivalent characterizations of Birkhoff-James orthogonality of compact linear operators in the complex case‎, ‎in order to distinguish the complex case from the real case‎.Sat, 10 Mar 2018 20:30:00 +0100The Bishop-Phelps-Bollobás modulus for functionals on classical Banach spaces
http://www.aot-math.org/article_58504_0.html
‎In this manuscript we compute the Bishop-Phelps-Bollob'as modulus for functionals in classical Banach spaces‎, ‎such as Hilbert spaces‎, ‎spaces of continuous functions‎, ‎$c_0$ and $ell_1$‎.
Sat, 10 Mar 2018 20:30:00 +0100Semicircular-like and semicircular laws on Banach $*$-probability spaces induced by dynamical ...
http://www.aot-math.org/article_58535_0.html
‎Starting from the finite Adele ring $A_{Bbb{Q}},$ we construct semigroup‎ ‎dynamical systems of $A_{Bbb{Q}},$ acting on certain $C^{*}$-probability‎ ‎spaces‎. ‎From such dynamical-systematic $C^{*}$-probability spaces‎, ‎we‎ ‎construct Banach-space operators acting on the $C^{*}$-probability spaces‎, ‎and corresponding Banach $*$-probability spaces‎. ‎In particular‎, ‎we are‎ ‎interested in Banach-space operators whose free distributions are the‎ ‎(weighted-)semicircular law(s)‎.Sun, 11 Mar 2018 20:30:00 +0100Banach partial $*$-algebras: an overview
http://www.aot-math.org/article_59546_0.html
A Banach partial $*$-algebra is a locally convex partial $*$-algebra whose total space is a Banach space. A Banach partial $*$-algebra is said to be of type (B) if it possesses a generating family of multiplier spaces that are also Banach spaces. We describe the basic properties of these objects and display a number of examples, namely $L^p$-like function spaces and spaces of operators on Hilbert scales or lattices. Finally we analyze the important cases of Banach quasi $*$-algebras and $CQ^*$-algebras.Tue, 13 Mar 2018 20:30:00 +0100