Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3220180401Different type of fixed point theorem for multivalued mappings3263364894510.15352/aot.1704-1153ENNour El Houda BouzaraVatan KarakayaJournal Article20170423In 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.http://www.aot-math.org/article_48945_9a630a7df83ea7e2437dc2f66697339d.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3220180401Singular Riesz measures on symmetric cones3373505005810.15352/aot.1706-1183ENAbdelhamid HassairiSfax universitySallouha LajmiSfax UniversityJournal Article20170621A 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.http://www.aot-math.org/article_50058_51185ec36d83d342d317bbc77469dfc9.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3220180401Cover topologies, subspaces, and quotients for some spaces of vector-valued functions3513645102010.15352/aot.1706-1177ENTerje HoimWilkes Honors College
Florida Atlantic University
Jupiter, FL 33458David RobbinsTrinity College
Hartford, CT 06106Journal Article20170610Let $X$ 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 $mathcal{D}$.http://www.aot-math.org/article_51020_60279e56eda0cbf7a35f61829763ebe5.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3220180401Integral representations and asymptotic behaviour of a Mittag-Leffler type function of two variables3653735111010.15352/apt.1705-1167ENChristian LavaultLIPN, CNRS UMR 7030, Universite Paris 13, Sorbonne Paris Cite,
F-93430 Villetaneuse, France.Journal Article20170526Integral 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.http://www.aot-math.org/article_51110_7b285ff8ff5c740337d228c0c47fdd15.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3220180401Operator algebras associated to modules over an integral domain3743875111910.15352/aot.1706-1181ENBenton DuncanDepartment of Mathematics, North Dakota State University, Fargo, North Dakota, USAJournal Article20170615We 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.http://www.aot-math.org/article_51119_929777a0cb213c0b5b50c5e587f49eb8.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3220180401On the truncated two-dimensional moment problem3883995118110.15352/aot.1708-1212ENSergey ZagorodnyukV. N. Karazin Kharkiv National University
School of Mathematics and Computer Sciences
Department of Higher Mathematics and Informatics
Svobody Square 4, 61022, Kharkiv, UkraineJournal Article20170804We 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.http://www.aot-math.org/article_51181_e83e76bde83920b1d8fc1a07b6244513.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3220180401Compactness of a class of radial operators on weighted Bergman spaces4004105130210.15352/aot.1707-1202ENYucheng LiHebei Normal UniversityMaofa WangWuhan UniversityWenhua LanJournal Article20170721In 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 $T_z$.http://www.aot-math.org/article_51302_439d50ac894977e6e3ff676eeb386a76.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3220180401Extensions of theory of regular and weak regular splittings to singular matrices4114225146710.15352/aot.1706-1188ENLitismita JenaSchool of Basic Sciences, Indian Institute of Technology Bhubaneswar,
Bhubaneswar - 751 013, Odisha, IndiaJournal Article20170626Matrix 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.http://www.aot-math.org/article_51467_a71852e0f00e9edd90f7d4e69b34141b.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3220180401On linear maps preserving certain pseudospectrum and condition spectrum subsets4234325146010.15352/aot.1705-1159ENSayda RagoubiDepartment of Mathematic, Univercity of Monastir, Preparatory Institute for Engineering Studies of Monastir, TunisiaJournal Article20170504 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< varepsilonhttp://www.aot-math.org/article_51460_43332c93297a57ce21f16a69e9f0e63e.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3220180401Certain geometric structures of $Lambda$-sequence spaces4334505341210.15352/aot.1705-1164ENAtanu MannaIndian Institute of Carpet Technology, Chauri road, Bhadohi-221401, Uttar Pradesh, India.Journal Article20170515The $Lambda$-sequence spaces $Lambda_p$ for $1< pleqinfty$ and their generalized forms $Lambda_{hat{p}}$ for $1http://www.aot-math.org/article_53412_20d5ffb6fef2fbf6e9bc4e0d2d893f7e.pdf