Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
1
2
2016
12
01
Norm inequalities for elementary operators related to contractions and operators with spectra contained in the unit disk in norm ideals
147
159
EN
Stefan
Milosevic
stefanm@matf.bg.ac.rs
10.22034/aot.1609.1019
If $A,Bin{mathcal B}({mathcal H})$ are normal contractions, then for every $Xin {mathcal C}_{left|!!;left|!!;left|cdotright|!!;right|!!;right|}({mathcal H})$ and $alpha > 0$ holdsbegin{equation}bigglvert!bigglvert!bigglvert Bigl(I - A^*ABigr)^{frac{alpha}{2}} X Bigl(I - B^*BBigr)^{frac{alpha}{2}} biggrvert !biggrvert !biggrvert leqslantbigglvert!bigglvert!bigglvert sum_{n=0}^infty (-1)^nbinom{alpha}{n}A^n X B^n biggrvert !biggrvert !biggrvert,end{equation}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.
Norm inequality,elementary operator,Q-norm
http://www.aot-math.org/article_40568.html
http://www.aot-math.org/article_40568_80909d5da8d38287a7b51d25a9389283.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
1
2
2016
12
01
Non-isomorphic C*-algebras with isomorphic unitary groups
160
163
EN
Ahmed
Al-Rawashdeh
aalrawashdeh@uaeu.ac.ae
10.22034/aot.1609.1004
H. 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 $*$-isomorphic
Banach algebra,C*-algebra,Unitary group
http://www.aot-math.org/article_40617.html
http://www.aot-math.org/article_40617_26e32bf3b4aae5a83e8011a9a7ef1fbb.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
1
2
2016
12
01
Approximation methods for solutions of system of split equilibrium problems
164
183
EN
Godwin
Chidi
Ugwunnadi
Department of Mathematics, Michael Okpara University of Agriculture,
Umudike, Abia State, Nigeria.
ugwunnadi4u@yahoo.com
Bashir
Ali
$Department of Mathematical Sciences, Bayero University Kano, P.M.B. 3011 Kano, Nigeria.
bashiralik@yahoo.com
10.22034/aot.1609.1018
In this paper, we introduce a new algorithm for finding a common fixed point of finitefamily of continuous pseudocontractive mappings which is a unique solution of somevariational inequality problem and whose image under some bounded linear operator isa common solution of some system of equilibrium problems in a real Hilbert space. Ourresult generalize and improve some well-known results.
Fixed point,split equilibrium problem,pseudocontractive mapping,strong monotone operator
http://www.aot-math.org/article_40716.html
http://www.aot-math.org/article_40716_7c0effcb326972cfdba73956c3068825.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
1
2
2016
12
01
Refinements of Holder-McCarthy inequality and Young inequality
184
188
EN
Masatoshi
Fujii
mfujii@cc.osaka-kyoiku.ac.jp
Ritsuo
Nakamoto
r-naka@net1.jway.ne.jp
10.22034/aot.1610.1037
We 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.
Holder-McCarthy inequality,Young inequality,convexity of functions
http://www.aot-math.org/article_40803.html
http://www.aot-math.org/article_40803_69372d74a3b8a8ae535e02e70d2fcb8d.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
1
2
2016
12
01
Existence results for approximate set-valued equilibrium problems
189
205
EN
Malek
Abbasi
malek.abbasi@sci.ui.ac.ir
Mahboubeh
Rezaei
mrezaie@sci.ui.ac.ir
10.22034/aot.1610.1034
This 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.
Set-valued equilibrium problems,KKM theorem,outer-semicontinuity,inner-semicontinuity,set-convergence
http://www.aot-math.org/article_40804.html
http://www.aot-math.org/article_40804_a9668eed8f400107c62dad3952217511.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
1
2
2016
12
01
Construction of a new class of quantum Markov fields
206
218
EN
Farrukh
Mukhamedov
United Arab Emirates University
far75m@yandex.ru
Luigi
Accardi
accardi@volterra.uniroma2.it
Abdessatar
Souissi
s.abdessatar@hotmail.fr
10.22034/aot.1610.1031
In 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.
Quantum Markov field,graph,tessellation,construction
http://www.aot-math.org/article_40859.html
http://www.aot-math.org/article_40859_e0cda11eb1f81c53a1e71cbdfc19e10e.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
1
2
2016
12
01
Tsallis relative operator entropy with negative parameters
219
235
EN
Yuki
Seo
Osaka Kyoiku University
yukis@cc.osaka-kyoiku.ac.jp
Jun Ichi
Fujii
Osaka Kyoiku University
fujii@cc.osaka-kyoiku.ac.jp
10.22034/aot.1610.1038
Tsallis 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.
Tsallis relative operator entropy,positive operator,operator geometric mean
http://www.aot-math.org/article_40901.html
http://www.aot-math.org/article_40901_63038f18f801ee19f7cb34323ff53c12.pdf