2018-06-24T02:10:46Z
http://www.aot-math.org/?_action=export&rf=summon&issue=6671
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
2
Different type of fixed point theorem for multivalued mappings
Nour El Houda
Bouzara
Vatan
Karakaya
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.
fixed point
Measure of noncompactness
Evolution inclusions
2018
04
01
326
336
http://www.aot-math.org/article_48945_9a630a7df83ea7e2437dc2f66697339d.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
2
Singular Riesz measures on symmetric cones
Abdelhamid
Hassairi
Sallouha
Lajmi
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.
Jordan algebra
symmetric cone
generalized power
Laplace transform
Riesz measure
2018
04
01
337
350
http://www.aot-math.org/article_50058_51185ec36d83d342d317bbc77469dfc9.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
2
Cover topologies, subspaces, and quotients for some spaces of vector-valued functions
Terje
Hoim
David
Robbins
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 $mathcal{D}$.
cover topology
bundle of Banach spaces
bundle of Banach algebras
2018
04
01
351
364
http://www.aot-math.org/article_51020_60279e56eda0cbf7a35f61829763ebe5.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
2
Integral representations and asymptotic behaviour of a Mittag-Leffler type function of two variables
Christian
Lavault
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.
Generalized two-parametric Mittag-Leffler type functions of two variables
Integral representations
Special functions
Hankel's integral contour
Asymptotic expansion formulas
2018
04
01
365
373
http://www.aot-math.org/article_51110_7b285ff8ff5c740337d228c0c47fdd15.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
2
Operator algebras associated to modules over an integral domain
Benton
Duncan
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.
semicrossed product
integral domain
module
2018
04
01
374
387
http://www.aot-math.org/article_51119_929777a0cb213c0b5b50c5e587f49eb8.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
2
On the truncated two-dimensional moment problem
Sergey
Zagorodnyuk
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.
moment problem
Hankel matrix
non-linear inequalities
2018
04
01
388
399
http://www.aot-math.org/article_51181_e83e76bde83920b1d8fc1a07b6244513.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
2
Compactness of a class of radial operators on weighted Bergman spaces
Yucheng
Li
Maofa
Wang
Wenhua
Lan
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 $T_z$.
Weighted Bergman space
radial operator
Berezin transform
compact operator
essential commutant
2018
04
01
400
410
http://www.aot-math.org/article_51302_439d50ac894977e6e3ff676eeb386a76.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
2
Extensions of theory of regular and weak regular splittings to singular matrices
Litismita
Jena
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.
Drazin inverse
group inverse
non-negativity
index-proper splittings
convergence theorem
comparison theorem
2018
04
01
411
422
http://www.aot-math.org/article_51467_a71852e0f00e9edd90f7d4e69b34141b.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
2
On linear maps preserving certain pseudospectrum and condition spectrum subsets
Sayda
Ragoubi
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
Linear preserver
condition spectrum
pseudospectrum
2018
04
01
423
432
http://www.aot-math.org/article_51460_43332c93297a57ce21f16a69e9f0e63e.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2018
3
2
Certain geometric structures of $Lambda$-sequence spaces
Atanu
Manna
The $Lambda$-sequence spaces $Lambda_p$ for $1< pleqinfty$ and their generalized forms $Lambda_{hat{p}}$ for $1
Cesaro sequence space
Nakano sequence space
James constant
von Neumann-Jordan constant
Extreme point
Kadec-Klee property
Hausdorff method
2018
04
01
433
450
http://www.aot-math.org/article_53412_20d5ffb6fef2fbf6e9bc4e0d2d893f7e.pdf