@Article{Milosevic2016,
author="Milosevic, Stefan",
title="Norm inequalities for elementary operators related to contractions and operators with spectra contained in the unit disk in norm ideals",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="2",
pages="147-159",
abstract="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.",
issn="2538-225X",
doi="10.22034/aot.1609.1019",
url="http://www.aot-math.org/article_40568.html"
}
@Article{Al-Rawashdeh2016,
author="Al-Rawashdeh, Ahmed",
title="Non-isomorphic C*-algebras with isomorphic unitary groups",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="2",
pages="160-163",
abstract="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",
issn="2538-225X",
doi="10.22034/aot.1609.1004",
url="http://www.aot-math.org/article_40617.html"
}
@Article{Ugwunnadi2016,
author="Ugwunnadi, Godwin Chidi
and Ali, Bashir",
title="Approximation methods for solutions of system of split equilibrium problems",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="2",
pages="164-183",
abstract="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.",
issn="2538-225X",
doi="10.22034/aot.1609.1018",
url="http://www.aot-math.org/article_40716.html"
}
@Article{Fujii2016,
author="Fujii, Masatoshi
and Nakamoto, Ritsuo",
title="Refinements of Holder-McCarthy inequality and Young inequality",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="2",
pages="184-188",
abstract="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.",
issn="2538-225X",
doi="10.22034/aot.1610.1037",
url="http://www.aot-math.org/article_40803.html"
}
@Article{Abbasi2016,
author="Abbasi, Malek
and Rezaei, Mahboubeh",
title="Existence results for approximate set-valued equilibrium problems",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="2",
pages="189-205",
abstract="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.",
issn="2538-225X",
doi="10.22034/aot.1610.1034",
url="http://www.aot-math.org/article_40804.html"
}
@Article{Mukhamedov2016,
author="Mukhamedov, Farrukh
and Accardi, Luigi
and Souissi, Abdessatar",
title="Construction of a new class of quantum Markov fields",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="2",
pages="206-218",
abstract="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.",
issn="2538-225X",
doi="10.22034/aot.1610.1031",
url="http://www.aot-math.org/article_40859.html"
}
@Article{Seo2016,
author="Seo, Yuki
and Fujii, Jun Ichi",
title="Tsallis relative operator entropy with negative parameters",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="2",
pages="219-235",
abstract="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.",
issn="2538-225X",
doi="10.22034/aot.1610.1038",
url="http://www.aot-math.org/article_40901.html"
}