Different type of fixed point theorem for multivalued mappings
Nour El Houda
Bouzara
author
Vatan
Karakaya
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
2
no.
2018
326
336
http://www.aot-math.org/article_48945_9a630a7df83ea7e2437dc2f66697339d.pdf
dx.doi.org/10.15352/aot.1704-1153
Singular Riesz measures on symmetric cones
Abdelhamid
Hassairi
Sfax university
author
Sallouha
Lajmi
Sfax University
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
2
no.
2018
337
350
http://www.aot-math.org/article_50058_51185ec36d83d342d317bbc77469dfc9.pdf
dx.doi.org/10.15352/aot.1706-1183
Cover topologies, subspaces, and quotients for some spaces of vector-valued functions
Terje
Hoim
Wilkes Honors College
Florida Atlantic University
Jupiter, FL 33458
author
David
Robbins
Trinity College
Hartford, CT 06106
author
text
article
2018
eng
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 $D\in \mathcal{D}$. 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 $\mathcal{D}$.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
2
no.
2018
351
364
http://www.aot-math.org/article_51020_60279e56eda0cbf7a35f61829763ebe5.pdf
dx.doi.org/10.15352/aot.1706-1177
Integral representations and asymptotic behaviour of a Mittag-Leffler type function of two variables
Christian
Lavault
LIPN, CNRS UMR 7030, Universite Paris 13, Sorbonne Paris Cite,
F-93430 Villetaneuse, France.
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
2
no.
2018
365
373
http://www.aot-math.org/article_51110_7b285ff8ff5c740337d228c0c47fdd15.pdf
dx.doi.org/10.15352/apt.1705-1167
Operator algebras associated to modules over an integral domain
Benton
Duncan
Department of Mathematics, North Dakota State University, Fargo, North Dakota, USA
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
2
no.
2018
374
387
http://www.aot-math.org/article_51119_929777a0cb213c0b5b50c5e587f49eb8.pdf
dx.doi.org/10.15352/aot.1706-1181
On the truncated two-dimensional moment problem
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
author
text
article
2018
eng
We study the truncated two-dimensional moment problem (with rectangular data) to find a non-negative measure $\mu(\delta)$, $\delta\in\mathfrak{B}(\mathbb{R}^2)$, such that $\int_{\mathbb{R}^2} x_1^m x_2^n d\mu = s_{m,n}$, $0\leq m\leq M,\quad 0\leq n\leq N$, where $\{ s_{m,n} \}_{0\leq m\leq M,\ 0\leq n\leq N}$ is a prescribed sequence of real numbers; $M,N\in\mathbb{Z}_+$. 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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
2
no.
2018
388
399
http://www.aot-math.org/article_51181_e83e76bde83920b1d8fc1a07b6244513.pdf
dx.doi.org/10.15352/aot.1708-1212
Compactness of a class of radial operators on weighted Bergman spaces
Yucheng
Li
Hebei Normal University
author
Maofa
Wang
Wuhan University
author
Wenhua
Lan
author
text
article
2018
eng
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 $T_z$.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
2
no.
2018
400
410
http://www.aot-math.org/article_51302_439d50ac894977e6e3ff676eeb386a76.pdf
dx.doi.org/10.15352/aot.1707-1202
Extensions of theory of regular and weak regular splittings to singular matrices
Litismita
Jena
School of Basic Sciences, Indian Institute of Technology Bhubaneswar,
Bhubaneswar - 751 013, Odisha, India
author
text
article
2018
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
2
no.
2018
411
422
http://www.aot-math.org/article_51467_a71852e0f00e9edd90f7d4e69b34141b.pdf
dx.doi.org/10.15352/aot.1706-1188
On linear maps preserving certain pseudospectrum and condition spectrum subsets
Sayda
Ragoubi
Department of Mathematic, Univercity of Monastir, Preparatory Institute for Engineering Studies of Monastir, Tunisia
author
text
article
2018
eng
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 : A\longrightarrow 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 : A\longrightarrow 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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
2
no.
2018
423
432
http://www.aot-math.org/article_51460_43332c93297a57ce21f16a69e9f0e63e.pdf
dx.doi.org/10.15352/aot.1705-1159
Certain geometric structures of $\Lambda$-sequence spaces
Atanu
Manna
Indian Institute of Carpet Technology, Chauri road, Bhadohi-221401, Uttar Pradesh, India.
author
text
article
2018
eng
The $\Lambda$-sequence spaces $\Lambda_p$ for $1< p\leq\infty$ and their generalized forms $\Lambda_{\hat{p}}$ for $1<\hat{p}<\infty$, $\hat{p}=(p_n)$, $n\in \mathbb{N}_0$ are introduced. The James constants and strong $n$-th James constants of $\Lambda_p$ for $1<p\leq\infty$ 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 $\mathbb{R}^{n+1}$, $n\in \mathbb{N}_0$. 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 $x\in S(\Lambda_{\hat{p}})$ 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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
3
v.
2
no.
2018
433
450
http://www.aot-math.org/article_53412_20d5ffb6fef2fbf6e9bc4e0d2d893f7e.pdf
dx.doi.org/10.15352/aot.1705-1164