Norm inequalities for elementary operators related to contractions and operators with spectra contained in the unit disk in norm ideals
Stefan
Milosevic
author
text
article
2016
eng
If $A,B\in{\mathcal B}({\mathcal H})$ are normal contractions, then for every $X\in {\mathcal C}_{\left|\!\!\;\left|\!\!\;\left|\cdot\right|\!\!\;\right|\!\!\;\right|}({\mathcal H})$ and $\alpha > 0$ holds\begin{equation}\biggl\vert\!\biggl\vert\!\biggl\vert \Bigl(I - A^*A\Bigr)^{\frac{\alpha}{2}} X \Bigl(I - B^*B\Bigr)^{\frac{\alpha}{2}} \biggr\vert \!\biggr\vert \!\biggr\vert \leqslant\biggl\vert\!\biggl\vert\!\biggl\vert \sum_{n=0}^\infty (-1)^n\binom{\alpha}{n}A^n X B^n \biggr\vert \!\biggr\vert \!\biggr\vert,\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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
2
no.
2016
147
159
http://www.aot-math.org/article_40568_80909d5da8d38287a7b51d25a9389283.pdf
dx.doi.org/10.22034/aot.1609.1019
Non-isomorphic C*-algebras with isomorphic unitary groups
Ahmed
Al-Rawashdeh
author
text
article
2016
eng
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
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
2
no.
2016
160
163
http://www.aot-math.org/article_40617_26e32bf3b4aae5a83e8011a9a7ef1fbb.pdf
dx.doi.org/10.22034/aot.1609.1004
Approximation methods for solutions of system of split equilibrium problems
Godwin
Ugwunnadi
Department of Mathematics, Michael Okpara University of Agriculture,
Umudike, Abia State, Nigeria.
author
Bashir
Ali
$Department of Mathematical Sciences, Bayero University Kano, P.M.B. 3011 Kano, Nigeria.
author
text
article
2016
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
2
no.
2016
164
183
http://www.aot-math.org/article_40716_7c0effcb326972cfdba73956c3068825.pdf
dx.doi.org/10.22034/aot.1609.1018
Refinements of Holder-McCarthy inequality and Young inequality
Masatoshi
Fujii
author
Ritsuo
Nakamoto
author
text
article
2016
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
2
no.
2016
184
188
http://www.aot-math.org/article_40803_69372d74a3b8a8ae535e02e70d2fcb8d.pdf
dx.doi.org/10.22034/aot.1610.1037
Existence results for approximate set-valued equilibrium problems
Malek
Abbasi
author
Mahboubeh
Rezaei
author
text
article
2016
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
2
no.
2016
189
205
http://www.aot-math.org/article_40804_a9668eed8f400107c62dad3952217511.pdf
dx.doi.org/10.22034/aot.1610.1034
Construction of a new class of quantum Markov fields
Farrukh
Mukhamedov
United Arab Emirates University
author
Luigi
Accardi
author
Abdessatar
Souissi
author
text
article
2016
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
2
no.
2016
206
218
http://www.aot-math.org/article_40859_e0cda11eb1f81c53a1e71cbdfc19e10e.pdf
dx.doi.org/10.22034/aot.1610.1031
Tsallis relative operator entropy with negative parameters
Yuki
Seo
Osaka Kyoiku University
author
Jun Ichi
Fujii
Osaka Kyoiku University
author
text
article
2016
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
2
no.
2016
219
235
http://www.aot-math.org/article_40901_63038f18f801ee19f7cb34323ff53c12.pdf
dx.doi.org/10.22034/aot.1610.1038