Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X1220161201Norm inequalities for elementary operators related to contractions and operators with spectra contained in the unit disk in norm ideals1471594056810.22034/aot.1609.1019ENStefan MilosevicJournal Article20160929If $A,Bin{mathcal B}({mathcal H})$ are normal contractions, then for every $Xin {mathcal C}_{left|!!;left|!!;left|cdotright|!!;right|!!;right|}({mathcal H})$ and $alpha > 0$ holds<br />begin{equation}<br />bigglvert!bigglvert!bigglvert Bigl(I - A^*ABigr)^{frac{alpha}{2}} X Bigl(I - B^*BBigr)^{frac{alpha}{2}} biggrvert !biggrvert !biggrvert leqslant<br />bigglvert!bigglvert!bigglvert sum_{n=0}^infty (-1)^nbinom{alpha}{n}A^n X B^n biggrvert !biggrvert !biggrvert,<br />end{equation}<br />which generalizes a result of D.R. Joci'c [Proc. Amer. Math. Soc. 126 (1998), no. 9, 2705--2713] for $alpha$ not being an integer. Similar inequalities in the Schatten $p$-norms, for non-normal $A,B$ and in the $Q$-norms if one of $A$ or $B$ is normal, are also given.http://www.aot-math.org/article_40568_80909d5da8d38287a7b51d25a9389283.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X1220161201Non-isomorphic C*-algebras with isomorphic unitary groups1601634061710.22034/aot.1609.1004ENAhmed Al-RawashdehJournal Article20160920H. Dye proved that the discrete unitary group in a factor determines the algebraic type of the factor. Afterwards, for a large class of simple unital $C^*$-algebras, Al-Rawashdeh, Booth and Giordano proved that the algebras are $*$-isomorphic if and only if their unitary groups are isomomorphic as abstract groups. In this paper, we give a counter example in the non-simple case. Indeed, we give two $C^*$-algebras with isomorphic unitary groups but the algebras themselves are not $*$-isomorphichttp://www.aot-math.org/article_40617_26e32bf3b4aae5a83e8011a9a7ef1fbb.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X1220161201Approximation methods for solutions of system of split equilibrium problems1641834071610.22034/aot.1609.1018ENGodwin ChidiUgwunnadiDepartment of Mathematics, Michael Okpara University of Agriculture,
Umudike, Abia State, Nigeria.Bashir Ali$Department of Mathematical Sciences, Bayero University Kano, P.M.B. 3011 Kano, Nigeria.Journal Article20161003In this paper, we introduce a new algorithm for finding a common fixed point of finite<br />family of continuous pseudocontractive mappings which is a unique solution of some<br />variational inequality problem and whose image under some bounded linear operator is<br />a common solution of some system of equilibrium problems in a real Hilbert space. Our<br />result generalize and improve some well-known results.http://www.aot-math.org/article_40716_7c0effcb326972cfdba73956c3068825.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X1220161201Refinements of Holder-McCarthy inequality and Young inequality1841884080310.22034/aot.1610.1037ENMasatoshi FujiiRitsuo NakamotoJournal Article20161024We refine the Holder-McCarthy inequality. The point is the convexity of the function induced by Holder-McCarthy inequality. Also we discuss the equivalent between refined Holder-McCarthy inequality and refined Young inequality with type of Kittaneh and Manasrah.http://www.aot-math.org/article_40803_69372d74a3b8a8ae535e02e70d2fcb8d.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X1220161201Existence results for approximate set-valued equilibrium problems1892054080410.22034/aot.1610.1034ENMalek AbbasiMahboubeh RezaeiJournal Article20161016This paper studies the generalized approximate set-valued equilibrium problems and furnishes some new existence results. The existence results for solutions are derived by using the celebrated KKM theorem and some concepts associated with the semi-continuity of the set-valued mappings such as outer-semicontinuity, inner-semicontinuity, upper-semicontinuity and so forth. The results achieved in this paper generalize and improve the works of many authors in references.http://www.aot-math.org/article_40804_a9668eed8f400107c62dad3952217511.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X1220161201Construction of a new class of quantum Markov fields2062184085910.22034/aot.1610.1031ENFarrukh MukhamedovUnited Arab Emirates UniversityLuigi AccardiAbdessatar SouissiJournal Article20161013In the present paper, we propose a new construction of quantum Markov fields on arbitrary connected, infinite, locally finite graphs. The construction is based on a specific tessellation on the considered graph, it allows us to express the Markov property for the local structure of the graph. Our main result is the existence and uniqueness of quantum Markov field.http://www.aot-math.org/article_40859_e0cda11eb1f81c53a1e71cbdfc19e10e.pdfTusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X1220161201Tsallis relative operator entropy with negative parameters2192354090110.22034/aot.1610.1038ENYuki SeoOsaka Kyoiku UniversityJun Ichi FujiiOsaka Kyoiku UniversityJournal Article20161026Tsallis relative operator entropy was firstly formulated by Fujii and Kamei as an operator version of Uhlmann's relative entropy. Afterwards, Yanagi, Kuriyama and Furuichi reformulated Tsallis relative operator entropy as an operator version of Tsallis relative entropy. In this paper, we define Tsallis relative operator entropy with negative parameters of (non-invertible) positive operators on a Hilbert space and show some properties.http://www.aot-math.org/article_40901_63038f18f801ee19f7cb34323ff53c12.pdf