2016
1
2
2
89
Norm inequalities for elementary operators related to contractions and operators with spectra contained in the unit disk in norm ideals
2
2
If $A,Bin{mathcal B}({mathcal H})$ are normal contractions, then for every $Xin {mathcal C}_{left!!;left!!;leftcdotright!!;right!!;right}({mathcal H})$ 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, 27052713] for $alpha$ not being an integer. Similar inequalities in the Schatten $p$norms, for nonnormal $A,B$ and in the $Q$norms if one of $A$ or $B$ is normal, are also given.
1

147
159


Stefan
Milosevic
Serbia
stefanm@matf.bg.ac.rs
Norm inequality
elementary operator
Qnorm
Nonisomorphic C*algebras with isomorphic unitary groups
2
2
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, AlRawashdeh, 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 nonsimple case. Indeed, we give two $C^*$algebras with isomorphic unitary groups but the algebras themselves are not $*$isomorphic
1

160
163


Ahmed
AlRawashdeh
United Arab Emirates
aalrawashdeh@uaeu.ac.ae
Banach algebra
C*algebra
Unitary group
Approximation methods for solutions of system of split equilibrium problems
2
2
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 wellknown results.
1

164
183


Godwin
Ugwunnadi
Department of Mathematics, Michael Okpara University of Agriculture,
Umudike, Abia State, Nigeria.
Department of Mathematics, Michael Okpara
Nigeria
ugwunnadi4u@yahoo.com


Bashir
Ali
$Department of Mathematical Sciences, Bayero University Kano, P.M.B. 3011 Kano, Nigeria.
$Department of Mathematical Sciences, Bayero
Nigeria
bashiralik@yahoo.com
fixed point
split equilibrium problem
pseudocontractive mapping
strong monotone operator
Refinements of HolderMcCarthy inequality and Young inequality
2
2
We refine the HolderMcCarthy inequality. The point is the convexity of the function induced by HolderMcCarthy inequality. Also we discuss the equivalent between refined HolderMcCarthy inequality and refined Young inequality with type of Kittaneh and Manasrah.
1

184
188


Masatoshi
Fujii
Japan
mfujii@cc.osakakyoiku.ac.jp


Ritsuo
Nakamoto
Japan
rnaka@net1.jway.ne.jp
HolderMcCarthy inequality
Young inequality
convexity of functions
Existence results for approximate setvalued equilibrium problems
2
2
This paper studies the generalized approximate setvalued 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 semicontinuity of the setvalued mappings such as outersemicontinuity, innersemicontinuity, uppersemicontinuity and so forth. The results achieved in this paper generalize and improve the works of many authors in references.
1

189
205


Malek
Abbasi
Iran
malek.abbasi@sci.ui.ac.ir


Mahboubeh
Rezaei
Iran
mrezaie@sci.ui.ac.ir
Setvalued equilibrium problems
KKM theorem
outersemicontinuity
innersemicontinuity
setconvergence
Construction of a new class of quantum Markov fields
2
2
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.
1

206
218


Farrukh
Mukhamedov
United Arab Emirates University
United Arab Emirates University
United Arab Emirates
far75m@yandex.ru


Luigi
Accardi
Italy
accardi@volterra.uniroma2.it


Abdessatar
Souissi
Tunisia
s.abdessatar@hotmail.fr
Quantum Markov field
graph
tessellation
Construction
Tsallis relative operator entropy with negative parameters
2
2
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 (noninvertible) positive operators on a Hilbert space and show some properties.
1

219
235


Yuki
Seo
Osaka Kyoiku University
Osaka Kyoiku University
Japan
yukis@cc.osakakyoiku.ac.jp


Jun Ichi
Fujii
Osaka Kyoiku University
Osaka Kyoiku University
Japan
fujii@cc.osakakyoiku.ac.jp
Tsallis relative operator entropy
positive operator
operator geometric mean