2018-04-22T03:22:43Z
http://www.aot-math.org/?_action=export&rf=summon&issue=4619
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
2
Norm inequalities for elementary operators related to contractions and operators with spectra contained in the unit disk in norm ideals
Stefan
Milosevic
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
2016
12
01
147
159
http://www.aot-math.org/article_40568_80909d5da8d38287a7b51d25a9389283.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
2
Non-isomorphic C*-algebras with isomorphic unitary groups
Ahmed
Al-Rawashdeh
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
2016
12
01
160
163
http://www.aot-math.org/article_40617_26e32bf3b4aae5a83e8011a9a7ef1fbb.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
2
Approximation methods for solutions of system of split equilibrium problems
Godwin
Ugwunnadi
Bashir
Ali
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
2016
12
01
164
183
http://www.aot-math.org/article_40716_7c0effcb326972cfdba73956c3068825.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
2
Refinements of Holder-McCarthy inequality and Young inequality
Masatoshi
Fujii
Ritsuo
Nakamoto
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
2016
12
01
184
188
http://www.aot-math.org/article_40803_69372d74a3b8a8ae535e02e70d2fcb8d.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
2
Existence results for approximate set-valued equilibrium problems
Malek
Abbasi
Mahboubeh
Rezaei
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
2016
12
01
189
205
http://www.aot-math.org/article_40804_a9668eed8f400107c62dad3952217511.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
2
Construction of a new class of quantum Markov fields
Farrukh
Mukhamedov
Luigi
Accardi
Abdessatar
Souissi
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
2016
12
01
206
218
http://www.aot-math.org/article_40859_e0cda11eb1f81c53a1e71cbdfc19e10e.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
2
Tsallis relative operator entropy with negative parameters
Yuki
Seo
Jun Ichi
Fujii
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
2016
12
01
219
235
http://www.aot-math.org/article_40901_63038f18f801ee19f7cb34323ff53c12.pdf