Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
2
2018
04
01
Different type of fixed point theorem for multivalued mappings
326
336
EN
Nour El Houda
Bouzara
bzr.nour@gmail.com
Vatan
Karakaya
vkkaya@yahoo.com
10.15352/aot.1704-1153
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.<br /><br />
fixed point,Measure of noncompactness,Evolution inclusions
http://www.aot-math.org/article_48945.html
http://www.aot-math.org/article_48945_9a630a7df83ea7e2437dc2f66697339d.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
2
2018
04
01
Singular Riesz measures on symmetric cones
337
350
EN
Abdelhamid
Hassairi
Sfax university
abdelhamid.hassairi@fss.rnu.tn
Sallouha
Lajmi
Sfax University
sallouha.lajmi@enis.tn
10.15352/aot.1706-1183
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
http://www.aot-math.org/article_50058.html
http://www.aot-math.org/article_50058_51185ec36d83d342d317bbc77469dfc9.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
2
2018
04
01
Cover topologies, subspaces, and quotients for some spaces of vector-valued functions
351
364
EN
Terje
Hoim
Wilkes Honors College
Florida Atlantic University
Jupiter, FL 33458
thoim@fau.edu
David
Robbins
Trinity College
Hartford, CT 06106
david.robbins@trincoll.edu
10.15352/aot.1706-1177
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
http://www.aot-math.org/article_51020.html
http://www.aot-math.org/article_51020_60279e56eda0cbf7a35f61829763ebe5.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
2
2018
04
01
Integral representations and asymptotic behaviour of a Mittag-Leffler type function of two variables
365
373
EN
Christian
Lavault
LIPN, CNRS UMR 7030, Universite Paris 13, Sorbonne Paris Cite,
F-93430 Villetaneuse, France.
lavault@lipn.univ-paris13.fr
10.15352/apt.1705-1167
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.<br />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
http://www.aot-math.org/article_51110.html
http://www.aot-math.org/article_51110_7b285ff8ff5c740337d228c0c47fdd15.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
2
2018
04
01
Operator algebras associated to modules over an integral domain
374
387
EN
Benton
Duncan
Department of Mathematics, North Dakota State University, Fargo, North Dakota, USA
benton.duncan@ndsu.edu
10.15352/aot.1706-1181
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
http://www.aot-math.org/article_51119.html
http://www.aot-math.org/article_51119_929777a0cb213c0b5b50c5e587f49eb8.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
2
2018
04
01
On the truncated two-dimensional moment problem
388
399
EN
Sergey
Zagorodnyuk
V. N. Karazin Kharkiv National University
School of Mathematics and Computer Sciences
Department of Higher Mathematics and Informatics
Svobody Square 4, 61022, Kharkiv, Ukraine
sergey.m.zagorodnyuk@gmail.com
10.15352/aot.1708-1212
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
http://www.aot-math.org/article_51181.html
http://www.aot-math.org/article_51181_e83e76bde83920b1d8fc1a07b6244513.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
2
2018
04
01
Compactness of a class of radial operators on weighted Bergman spaces
400
410
EN
Yucheng
Li
Hebei Normal University
liyucheng@hebtu.edu.cn
Maofa
Wang
Wuhan University
whuwmf@163.com
Wenhua
Lan
lanwenhua2006@126.com
10.15352/aot.1707-1202
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
http://www.aot-math.org/article_51302.html
http://www.aot-math.org/article_51302_439d50ac894977e6e3ff676eeb386a76.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
2
2018
04
01
Extensions of theory of regular and weak regular splittings to singular matrices
411
422
EN
Litismita
Jena
School of Basic Sciences, Indian Institute of Technology Bhubaneswar,
Bhubaneswar - 751 013, Odisha, India
litumath@gmail.com
10.15352/aot.1706-1188
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
http://www.aot-math.org/article_51467.html
http://www.aot-math.org/article_51467_a71852e0f00e9edd90f7d4e69b34141b.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
2
2018
04
01
On linear maps preserving certain pseudospectrum and condition spectrum subsets
423
432
EN
Sayda
Ragoubi
Department of Mathematic, Univercity of Monastir, Preparatory Institute for Engineering Studies of Monastir, Tunisia
ragoubis@yahoo.fr
10.15352/aot.1705-1159
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:<br /> (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.<br />(2) Let $A$ and $B$ be complex unital Banach algebras and $0< varepsilon<1$. Let $phi : Alongrightarrow B $ be unital linear map. Then<br />(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 $a in A$.<br />(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.<br /><br />
Linear preserver,condition spectrum,pseudospectrum
http://www.aot-math.org/article_51460.html
http://www.aot-math.org/article_51460_43332c93297a57ce21f16a69e9f0e63e.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
3
2
2018
04
01
Certain geometric structures of $Lambda$-sequence spaces
433
450
EN
Atanu
Manna
Indian Institute of Carpet Technology, Chauri road, Bhadohi-221401, Uttar Pradesh, India.
atanuiitkgp86@gmail.com
10.15352/aot.1705-1164
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.
Cesaro sequence space,Nakano sequence space,James constant,von Neumann-Jordan constant,Extreme point,Kadec-Klee property,Hausdorff method
http://www.aot-math.org/article_53412.html
http://www.aot-math.org/article_53412_20d5ffb6fef2fbf6e9bc4e0d2d893f7e.pdf