eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
2
147
159
10.22034/aot.1609.1019
40568
Norm inequalities for elementary operators related to contractions and operators with spectra contained in the unit disk in norm ideals
Stefan Milosevic
stefanm@matf.bg.ac.rs
1
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 $alpha > 0$ 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.pdf
Norm inequality
elementary operator
Q-norm
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
2
160
163
10.22034/aot.1609.1004
40617
Non-isomorphic C*-algebras with isomorphic unitary groups
Ahmed Al-Rawashdeh
aalrawashdeh@uaeu.ac.ae
1
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
http://www.aot-math.org/article_40617_26e32bf3b4aae5a83e8011a9a7ef1fbb.pdf
Banach algebra
C*-algebra
Unitary group
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
2
164
183
10.22034/aot.1609.1018
40716
Approximation methods for solutions of system of split equilibrium problems
Godwin Ugwunnadi
ugwunnadi4u@yahoo.com
1
Bashir Ali
bashiralik@yahoo.com
2
Department of Mathematics, Michael Okpara University of Agriculture,
Umudike, Abia State, Nigeria.
$Department of Mathematical Sciences, Bayero University Kano, P.M.B. 3011 Kano, Nigeria.
In 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.pdf
fixed point
split equilibrium problem
pseudocontractive mapping
strong monotone operator
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
2
184
188
10.22034/aot.1610.1037
40803
Refinements of Holder-McCarthy inequality and Young inequality
Masatoshi Fujii
mfujii@cc.osaka-kyoiku.ac.jp
1
Ritsuo Nakamoto
r-naka@net1.jway.ne.jp
2
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.
http://www.aot-math.org/article_40803_69372d74a3b8a8ae535e02e70d2fcb8d.pdf
Holder-McCarthy inequality
Young inequality
convexity of functions
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
2
189
205
10.22034/aot.1610.1034
40804
Existence results for approximate set-valued equilibrium problems
Malek Abbasi
malek.abbasi@sci.ui.ac.ir
1
Mahboubeh Rezaei
mrezaie@sci.ui.ac.ir
2
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.
http://www.aot-math.org/article_40804_a9668eed8f400107c62dad3952217511.pdf
Set-valued equilibrium problems
KKM theorem
outer-semicontinuity
inner-semicontinuity
set-convergence
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
2
206
218
10.22034/aot.1610.1031
40859
Construction of a new class of quantum Markov fields
Farrukh Mukhamedov
far75m@yandex.ru
1
Luigi Accardi
accardi@volterra.uniroma2.it
2
Abdessatar Souissi
s.abdessatar@hotmail.fr
3
United Arab Emirates University
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.
http://www.aot-math.org/article_40859_e0cda11eb1f81c53a1e71cbdfc19e10e.pdf
Quantum Markov field
Graph
tessellation
Construction
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
2
219
235
10.22034/aot.1610.1038
40901
Tsallis relative operator entropy with negative parameters
Yuki Seo
yukis@cc.osaka-kyoiku.ac.jp
1
Jun Ichi Fujii
fujii@cc.osaka-kyoiku.ac.jp
2
Osaka Kyoiku University
Osaka Kyoiku University
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.
http://www.aot-math.org/article_40901_63038f18f801ee19f7cb34323ff53c12.pdf
Tsallis relative operator entropy
positive operator
operator geometric mean