ORIGINAL_ARTICLE
Norm inequalities for elementary operators related to contractions and operators with spectra contained in the unit disk in norm ideals
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.
http://www.aot-math.org/article_40568_80909d5da8d38287a7b51d25a9389283.pdf
2016-12-01T11:23:20
2017-11-18T11:23:20
147
159
10.22034/aot.1609.1019
Norm inequality
elementary operator
Q-norm
Stefan
Milosevic
stefanm@matf.bg.ac.rs
true
1
LEAD_AUTHOR
ORIGINAL_ARTICLE
Non-isomorphic C*-algebras with isomorphic unitary groups
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
2016-12-01T11:23:20
2017-11-18T11:23:20
160
163
10.22034/aot.1609.1004
Banach algebra
C*-algebra
Unitary group
Ahmed
Al-Rawashdeh
aalrawashdeh@uaeu.ac.ae
true
1
LEAD_AUTHOR
ORIGINAL_ARTICLE
Approximation methods for solutions of system of split equilibrium problems
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.
http://www.aot-math.org/article_40716_7c0effcb326972cfdba73956c3068825.pdf
2016-12-01T11:23:20
2017-11-18T11:23:20
164
183
10.22034/aot.1609.1018
Fixed point
split equilibrium problem
pseudocontractive mapping
strong monotone operator
Godwin
Ugwunnadi
ugwunnadi4u@yahoo.com
true
1
Department of Mathematics, Michael Okpara University of Agriculture,
Umudike, Abia State, Nigeria.
Department of Mathematics, Michael Okpara University of Agriculture,
Umudike, Abia State, Nigeria.
Department of Mathematics, Michael Okpara University of Agriculture,
Umudike, Abia State, Nigeria.
LEAD_AUTHOR
Bashir
Ali
bashiralik@yahoo.com
true
2
$Department of Mathematical Sciences, Bayero University Kano, P.M.B. 3011 Kano, Nigeria.
$Department of Mathematical Sciences, Bayero University Kano, P.M.B. 3011 Kano, Nigeria.
$Department of Mathematical Sciences, Bayero University Kano, P.M.B. 3011 Kano, Nigeria.
AUTHOR
ORIGINAL_ARTICLE
Refinements of Holder-McCarthy inequality and Young inequality
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
2016-12-01T11:23:20
2017-11-18T11:23:20
184
188
10.22034/aot.1610.1037
Holder-McCarthy inequality
Young inequality
convexity of functions
Masatoshi
Fujii
mfujii@cc.osaka-kyoiku.ac.jp
true
1
LEAD_AUTHOR
Ritsuo
Nakamoto
r-naka@net1.jway.ne.jp
true
2
AUTHOR
ORIGINAL_ARTICLE
Existence results for approximate set-valued equilibrium problems
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
2016-12-01T11:23:20
2017-11-18T11:23:20
189
205
10.22034/aot.1610.1034
Set-valued equilibrium problems
KKM theorem
outer-semicontinuity
inner-semicontinuity
set-convergence
Malek
Abbasi
malek.abbasi@sci.ui.ac.ir
true
1
LEAD_AUTHOR
Mahboubeh
Rezaei
mrezaie@sci.ui.ac.ir
true
2
AUTHOR
ORIGINAL_ARTICLE
Construction of a new class of quantum Markov fields
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
2016-12-01T11:23:20
2017-11-18T11:23:20
206
218
10.22034/aot.1610.1031
Quantum Markov field
graph
tessellation
construction
Farrukh
Mukhamedov
far75m@yandex.ru
true
1
United Arab Emirates University
United Arab Emirates University
United Arab Emirates University
LEAD_AUTHOR
Luigi
Accardi
accardi@volterra.uniroma2.it
true
2
AUTHOR
Abdessatar
Souissi
s.abdessatar@hotmail.fr
true
3
AUTHOR
ORIGINAL_ARTICLE
Tsallis relative operator entropy with negative parameters
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
2016-12-01T11:23:20
2017-11-18T11:23:20
219
235
10.22034/aot.1610.1038
Tsallis relative operator entropy
positive operator
operator geometric mean
Yuki
Seo
yukis@cc.osaka-kyoiku.ac.jp
true
1
Osaka Kyoiku University
Osaka Kyoiku University
Osaka Kyoiku University
LEAD_AUTHOR
Jun Ichi
Fujii
fujii@cc.osaka-kyoiku.ac.jp
true
2
Osaka Kyoiku University
Osaka Kyoiku University
Osaka Kyoiku University
AUTHOR