2018-06-22T15:36:43Z
http://www.aot-math.org/?_action=export&rf=summon&issue=7516
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
Linear preservers of two-sided right matrix majorization on $mathbb{R}_{n}$
Ahmad
Mohammadhasani
Asma
Ilkhanizadeh Manesh
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].
Linear preserver
right matrix majorization
row stochastic matrix
2018
07
01
451
458
http://www.aot-math.org/article_53654_59d049b74ce0e9accb168ebb4db2105b.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
Pompeiu-Čebyšev type inequalities for selfadjoint operators in Hilbert spaces
Mohammad
Alomari
In this work, generalization of some inequalities for continuous h-synchronous (h-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved. .
Hilbert space
selfadjoint operators
h-synchronization
2018
07
01
459
472
http://www.aot-math.org/article_54087_0a5c931295412bb7ca2a95f8feda0573.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
Perturbation of minimum attaining operators
Jadav
Ganesh
Golla
Ramesh
Daniel
Sukumar
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.
minimum modulus
spectrum
essential spectrum
porous set
2018
07
01
473
490
http://www.aot-math.org/article_54270_bc17d5d42fb655dade72954a6c56fd0a.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
Besicovitch almost automorphic solutions of nonautonomous differential equations of first order
Marko
Kostic
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.
Besicovitch almost automorphic functions
weighted Besicovitch pseudo-almost automorphic functions
nonautonomous differential equations of first order
evolution systems
Green's functions
2018
07
01
491
506
http://www.aot-math.org/article_54492_65ee01700cc48f0cf7bef87718a3f617.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
A Kakutani-Mackey-like theorem
Marina
Haralampidou
Konstantinos
Tzironis
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.
(semi-)quasi-complemented linear space
quasi-complementor
pseudo-$H$-space
automorphically perfect pair
2018
07
01
507
521
http://www.aot-math.org/article_56029_e54f74797c92d1f650c19dab2b77f90e.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
$T1$ theorem for inhomogeneous Triebel--Lizorkin and Besov spaces on RD-spaces and its application
Fanghui
Liao
Zongguang
Liu
Hongbin
Wang
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.
T1 theorem
Triebel-Lizorkin space
Besov space
RD-space
2018
07
01
522
537
http://www.aot-math.org/article_57072_888f8c2b8da0ea7fac2ff9eeb211dc2a.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
Fixed points of a class of unitary operators
Namita
Das
Jitendra
Behera
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.
Right half plane
Bergman space
unitary operator
automorphism
fixed point
2018
07
01
538
550
http://www.aot-math.org/article_57403_9ef2e37b57c571444740ffc979926104.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
Well-posedness issues for a class of coupled nonlinear Schr"odinger equations with critical exponential growth
Hanen
Hezzi
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.
Nonlinear Schrodinger system
global well-posedness
scattering
blow-up
Moser-Trudinger inequality
2018
07
01
551
581
http://www.aot-math.org/article_57444_2c0e0da5d64c8fabde55e8ee06badb79.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
Closedness and invertibility for the sum of two closed operators
Nikolaos
Roidos
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.
Sectorial operators
bounded $H^{infty}$-calculus
maximal regularity
abstract Cauchy problem
2018
07
01
582
605
http://www.aot-math.org/article_57481_9dc50d9f66c3c3266ee8dd0c78d135ef.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
Parallel iterative methods for solving the common null point problem in Banach spaces
Tuyen
Truong
Nguyen
Trang
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.
Common null point problem
maximal monotone operator
generalized resolvent
$varepsilon$-enlargement
2018
07
01
606
619
http://www.aot-math.org/article_57735_78e447c015a1cc99204e72dafc32433e.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
Complex isosymmetric operators
Muneo
Chō
Ji Eun
Lee
T.
Prasad
Kôtarô
Tanahashi
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.
Isosymmetric operator
complex isosymmetric operator
complex symmetric operator
(m
C)-isometric operator
2018
07
01
620
631
http://www.aot-math.org/article_57759_b9d4decc8062d9cb38ddba2ce3edb0bc.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
Variant versions of the Lewent type determinantal inequality
Ali
Morassaei
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.
Lewent inequality
determinantal inequality
Jensen-Mercer inequality
trace class operators
contraction
2018
07
01
632
638
http://www.aot-math.org/article_58027_e4993959d2838f85d7a990cb957c644c.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
wUR modulus and normal structure in Banach spaces
Ji
Gao
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.
uniform convexity
normal structure
wUR
2018
07
01
639
646
http://www.aot-math.org/article_58068_bab5247b1aec6e648c85b7d2223d9400.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
The matrix power means and interpolations
DINH
Trung Hoa
Raluca
Dumitru
Jose A.
Franco
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.
Kubo-Ando means
Interpolation
arithmetic mean
geometric mean
harmonic mean
Heron means
Heinz means
power means
2018
07
01
647
654
http://www.aot-math.org/article_58111_2db06770ff58292e14a48df88a3e8429.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
$C^*$-algebra distance filters
Tristan
Bice
Alessandro
Vignati
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.
filter
$C^*$-algebra
compact projection
non-symmetric distance
2018
07
01
655
681
http://www.aot-math.org/article_58258_60253d2648889c6465fbb303065fad63.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
On Neugebauer's covering theorem
Jésus M.
Aldaz
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.
Uncentered maximal operator
restricted weak type
geometrically doubling
2018
07
01
682
689
http://www.aot-math.org/article_58259_27f6aa7b3ddc36299f175589a7784c20.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
The existence of hyper-invariant subspaces for weighted shift operators
Hossein
Sadeghi
Farzollah
Mirzapour
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.
invariant subspace
weighted space
shift operator
2018
07
01
690
698
http://www.aot-math.org/article_58113_86409cebe989bb55a3992eaaa911aa5a.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
Orthogonality of bounded linear operators on complex Banach spaces
Kallol
Paul
Debmalya
Sain
Arpita
Mal
Kalidas
Mandal
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.
Birkhoff-James orthogonality
complex Banach space
bounded linear operator
2018
07
01
699
709
http://www.aot-math.org/article_58482_7dbaeeafc2780dac3d0996c2d9a48612.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
Affine actions and the Yang-Baxter equation
Dilian
Yang
In this paper, the relations between the Yang-Baxter equation and affine actions are explored in detail. In particular, we classify the injective set-theoretic solutions of the Yang-Baxter equation in two ways: (i) by their associated affine actions of their structure groups on their derived structure groups, and (ii) by the $C^*$-dynamical systems obtained from their associated affine actions. On the way to our main results, several other useful results are also obtained.
Yang-Baxter equation
set-theoretic solution
affine action
C*-dynamical system
2018
07
01
710
730
http://www.aot-math.org/article_60104_5b1e93d062f80db45bd3e9f530226155.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
3
Characterizing projections among positive operators in the unit sphere
Antonio
Peralta
Let $E$ and $P$ be subsets of a Banach space $X$, and let us define the unit sphere around $E$ in $P$ as the set $$Sph(E;P) :=left{ xin P : |x-b|=1 hbox{ for all } bin E right}.$$ Given a $C^*$-algebra $A$ and a subset $Esubset A,$ we shall write $Sph^+ (E)$ or $Sph_A^+ (E)$ for the set $Sph(E;S(A^+)),$ where $S(A^+)$ denotes the unit sphere of $A^+$. We prove that, for every complex Hilbert space $H$, the following statements are equivalent for every positive element $a$ in the unit sphere of $B(H)$: (a) $a$ is a projection (b) $Sph^+_{B(H)} left( Sph^+_{B(H)}({a}) right) ={a}$. We also prove that the equivalence remains true when $B(H)$ is replaced with an atomic von Neumann algebra or with $K(H_2)$, where $H_2$ is an infinite-dimensional and separable complex Hilbert space. In the setting of compact operators we establish a stronger conclusion by showing that the identity $$Sph^+_{K(H_2)} left( Sph^+_{K(H_2)}(a) right) =left{ bin S(K(H_2)^+) : !! begin{array}{c}s_{_{K(H_2)}} (a) leq s_{_{K(H_2)}} (b), hbox{ and }\ textbf{1}-r_{_{B(H_2)}}(a)leq textbf{1}-r_{_{B(H_2)}}(b) end{array}right},$$ holds for every $a$ in the unit sphere of $K(H_2)^+$, where $r_{_{B(H_2)}}(a)$ and $s_{_{K(H_2)}} (a)$ stand for the range and support projections of $a$ in $B(H_2)$ and $K(H_2)$, respectively.
Projection
unit sphere around a subset
bounded linear operator
compact linear operator
2018
07
01
731
744
http://www.aot-math.org/article_60341_1b13a753583eb613f2eecd19bf0bb7e9.pdf