Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401Approximation by Chlodowsky variant of Szasz operators involving Sheffer polynomials3213416520710.15352/aot.1804-1350ENKhursheed AnsariDepartment of Mathematics, College of Science, King Khalid University, 61413, Abha, Saudi Arabia0000-0003-4564-6211M. MursaleenAligarh Muslim University, IndiaA.H. Al-AbiedDepartment of Mathematics, Aligarh Muslim University, Aligarh-202002,
IndiaJournal Article20180423In this article, we present a Chlodowsky type variation of Sz'{a}sz operators defined by means of the Sheffer type polynomials. We established convergence properties and the order of convergence through a classical approach, the second order modulus of continuity, Peetre's $K$-functional and a new type of weighted modulus of continuity. Furthermore, $A$-statistical approximation of Korokin type for the operators is also shown and the rate of convergence of operators for functions having derivatives of bounded variation is also obtained. Moreover, some numerical and graphical examples are also given to support our results.http://www.aot-math.org/article_65207_c6390ef821e65b33b2dade1903667b8c.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401Lie centralizers on triangular rings and nest algebras3423506645210.15352/aot.1804-1341ENAjda FosnerFaculty of Management, University of Primorska, Koper, SloveniaWu JingFayetteville State University, USAJournal Article20180402We introduce the definition of Lie centralizers and investigate the additivity of Lie centralizers on triangular rings. We also present characterizations of both centralizers and Lie centralizers on triangular rings and nest algebras.http://www.aot-math.org/article_66452_d8c578ce8ca7cbbcf9d7e56d4e9cd8cb.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401Partial isometries and a general spectral theorem3513686808610.15352/aot.1804-1355ENBela NagyBudapest University of Technology and Economics, HungaryJournal Article20180428We prove a general spectral theorem for an arbitrary densely defined closed linear operator $T$ between complex Hilbert spaces $H$ and $K$. The corresponding operator measure is partial isometry valued, and has properties similar to those of the resolution of the identity of a nonnegative self-adjoint operator. The main method is the use of the canonical factorization (polar decomposition) obtained by v. Neumann and Murray. The uniqueness of the generalized resolution of the identity is studied together with the properties of a (non-multiplicative) functional calculus. The properties of this generalized resolution of the identity are also investigated.http://www.aot-math.org/article_68086_437abd0d5d95979c4b8523bafe087891.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401Some classes of Banach spaces and complemented subspaces of operators3693876860810.15352/aot.1802-1318ENIoana GhenciuUniversity of Wisconsin River FallsJournal Article20180220The concept of $p$-$L$-limited sets and Banach spaces with the $p$-$L$-limited property ($1le p< infty$) are studied. Some characterizations of limited $p$-convergent operators are obtained. The complementability of some spaces of operators in the space of limited $p$-convergent operators is also investigated.http://www.aot-math.org/article_68608_116e1880d023e199e481734cd5c80e88.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401Compact embeddings on a subspace of weighted variable exponent Sobolev spaces3884056935410.15352/aot.1803-1335ENCihan UnalSinop University, TurkeyIsmail AydınSinop University, TurkeyJournal Article20180321In this paper, we define an intersection space between weighted classical Lebesgue spaces and weighted Sobolev spaces with variable exponent. We consider the basic properties of the space. Also, we investigate some inclusions, continuous embeddings and compact embeddings under somehttp://www.aot-math.org/article_69354_fec0d5b601cd31876b32261283526a44.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401A descriptive definition of the It^{o}-Henstock integral for the operator-valued stochastic process4064186961210.15352/aot.1808-1406ENMhelmar AvilaLabendiaDepartment of Mathematics and Statistics, College of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, 9200 Iligan City, PhilippinesJayrold ArcedeDepartment of Mathematics, College of Arts and Sciences, Caraga State University, 8600 Butuan City, PhilippinesJournal Article20180814In this paper, we formulate a version of Fundamental Theorem for the It$hat{text{o}}$-Henstock integral of an operator-valued stochastic process with respect to a Hilbert space-valued Wiener process. This theorem will give a descriptive definition of the It$hat{text{o}}$-Henstock integral for the operator-valued stochastic process.<br /> http://www.aot-math.org/article_69612_541d7eb81b030b9bc07d30e41c3cfb81.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401A note on irreducible representations of some vector-valued function algebras4194276970210.15352/aot.1805-1370ENTerje HoimWilkes Honors College Florida Atlantic University, EstoniaDavid RobbinsTrinity College, USAJournal Article20180518Let $pi :mathcal{E}$ $rightarrow X$ be a bundle of Banach algebras, where $X$ is a completely regular Hausdorff space. We identify the sets of irreducible representations of several topological subalgebras of $Gamma(pi ),$ the space of continuous sections of $pi .$ The results unify recent and older work of various authors regarding representations on algebra-valued function spaces.http://www.aot-math.org/article_69702_b05125c1a4e873fd6b6d490d5862ea4d.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401Monomial decomposition of homogeneous polynomials in vector lattices4284466973910.15352/aot.1807-1394ENAnatoly KusraevDepartment of Functional Analysis, Southern Mathematical Institute of Vladikavkaz Scientific Centre of Russian Academy of Sciences, Vladikavkaz, RussiaZalina KusraevaDepartment of Functional Analysis, Southern Mathematical Institute of Vladikavkaz Scientific Centre of Russian Academy of Sciences, Vladikavkaz, RussiaJournal Article20180704The paper is devoted to the characterization and weighted shift representation of regular homogeneous polynomials between vector lattices admitting a decomposition into a sum of monomials in lattice homomorphisms. The main tool is the factorization theorem for order bounded disjointness preserving multilinear operators obtained earlier by the authors.http://www.aot-math.org/article_69739_02cf7b81af9ff354576cb78f5dbf72c5.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401Multicentric holomorphic calculus for $n-$tuples of commuting operators4474617058710.15352/aot.1804-1346ENDiana ElenaAndreiDepartment of Mathematics and Systems Analysis, Aalto University, Otaniemi, Finland0000-0001-9449-052XJournal Article20180416In multicentric holomorphic calculus, one represents the function $varphi$ using a new polynomial variable $w=p(z),$ $zin mathbb{C},$ in such a way that when it is evaluated at the operator $T,$ then $p(T)$ is small in norm. Usually it is assumed that $p$ has distinct roots. In this paper we aim to extend this multicentric holomorphic calculus to $n-$tuples of commuting operators looking in particular at the case when $n=2$.http://www.aot-math.org/article_70587_8a1158929babda87554886394d0544e4.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401A variational inequality theory for constrained problems in reflexive Banach spaces4624807385310.15352/aot.1809-1423ENTeffera M. AsfawDepartment of Mathematics, Virginia Polytechnic Institute and State University, USAJournal Article20180926Let $X$ be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space $X^*$ and $K$ be a nonempty, closed and convex subset of $X$. Let $T: Xsupseteq D(T)to 2^{X^*}$ be maximal monotone, $S: Kto 2^{X^*}$ be bounded and of type $(S_+)$ and $C: Xsupseteq D(C)to X^*$ with $D(T)cap D(partial phi)cap Ksubseteq D(C)$. Let $phi : Xto (-infty, infty]$ be a proper, convex and lower semicontinuous function. New existence theorems are proved for solvability of variational inequality problems of the type $rm{VIP}(T+S+C, K, phi, f^*)$ if $C$ is compact and $rm{VIP}(T+C, K, phi, f^*)$ if $T$ is of compact resolvent and, $C$ is bounded and continuous. Various improvements and generalizations of the existing results for $T+S$ and $phi$, are obtained. The theory is applied to prove existence of solution for nonlinear constrained variational inequality problems.http://www.aot-math.org/article_73853_5b20e42671d5ba3533c447a95e9f7bc5.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401$M$-operators on partially ordered Banach spaces4814967560110.15352/aot.1806-1383ENAnke KalauchInstitute for Analysis, Department of Mathematics, Technical University of Dresden, D - 01062 Dresden, Germany.Lavanya SuriyamoorthyDepartment of Mathematics,
Indian Institute of Technology Madras,
Chennai 600 036, India.SivaKumar K CIIT Madras, ChennaiJournal Article20180613For a matrix $A in mathbb{R}^{n times n}$ whose off-diagonal entries are nonpositive, there are several well-known properties that are equivalent to $A$ being an invertible $M$-matrix. One of them is the positive stability of $A$. A generalization of this characterization to partially ordered Banach spaces is considered in this article. Relationships with certain other equivalent conditions are derived. An important result on singular irreducible $M$-matrices is generalized using the concept of $M$-operators and irreducibility. Certain other invertibility conditions of $M$-operators are also investigated.http://www.aot-math.org/article_75601_fbd1b769fb3b985dfbb514304f15a1f8.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401Multiplicity of solutions for a class of Neumann elliptic systems in anisotropic Sobolev spaces with variable exponent4975137665310.15352/aot.1808-1409ENMoahmed Saad Bouh Elemine VallUniversity of Nouakchott Al Aasriya, MauritaniaAhmed AhmedUniversity of Nouakchott Al Aasriya, MauritaniaJournal Article20180824In this paper, we prove the existence of infinitely many solutions of a system of boundary value problems involving flux boundary conditions in anisotropic variable exponent Sobolev spaces, by applying a critical point variational principle obtained by Ricceri as a consequence of a more general variational principle and the theory of the anisotropic variable exponent Sobolev spaces.http://www.aot-math.org/article_76653_e45b9d36757ff57b6b8da4967e37f619.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401Existence of weak solutions for an infinite system of second order differential equations5145287716310.15352/aot.1807-1400ENFuli WangChangzhou University, China0000-0003-0034-7699Hua ZhouChangzhou University, ChinaShiyou WengSuzhou Vocational University, ChinaJournal Article20180722In this paper, we investigate the existence of weak solutions for a boundary value problem of an infinite system of second order differential equations. As the main tool, a new Krasnosel'skii type fixed point theorem in Fr'echet spaces is established in conjunction with the technique of measures of weak noncompactness.http://www.aot-math.org/article_77163_ddb2fdb9ae4eb5aa502bd67c73fe69a8.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401on Herz's extension theorem5295387738710.15352/aot.1809-1417ENAntoine DerighettiEcole Polytechnique de Lausanne, SwitzerlandJournal Article20180910{Large Abstract. We present a self-contained proof of the following famous extension theorem due to Carl Herz. A closed subgroup $H$ of a locally compact group $G$ is a set of $p$hskip1pt-synthesis in $G$ if and only for every hbox{$uin A_p(H)cap C_{00}(H)$} and for every $varepsilon >0$ there is hbox{$vin A_p(G)cap C_{00}(G),$} an extension of $u,$ such that$$|v|_{A_p(G)}http://www.aot-math.org/article_77387_885f1034ec558d864303f11ef951d552.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X4220190401Eigenvalue problems involving the fractional $p(x)$-Laplacian operator5395557813210.15352/aot.1809-1420ENElhoussine AZROULSidi Mohamed Ben Abdellah University, Morocco.Abdelmoujib BenkiraneSidi Mohamed Ben Abdellah University, Morocco.Mohammed SHIMISidi Mohamed Ben Abdellah University, Morocco.0000-0002-7306-6815Journal Article20180914http://www.aot-math.org/article_78132_afb195db0a27432779048fdb8c36198a.pdf