@Article{Ando2016,
author="Ando, Tsuyoshi",
title="Square inequality and strong order relation",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="1",
pages="1-7",
abstract="It is well-known that for Hilbert space linear operators $0 \leq A$ and $0 \leq C$, inequality$C \leq A$ does not imply $C^2 \leq A^2.$ We introduce a strong order relation $0 \leq B \lll A$, which guarantees that $C^2 \leq B^{1/2}AB^{1/2}\ \text{for all} \ 0 \leq C \leq B,$ and that $C^2 \leq A^2$ when $B$ commutes with $A$. Connections of this approach with the arithmetic-geometric mean inequality of Bhatia--Kittaneh as well as the Kantorovich constant of $A$ are mentioned.",
issn="2538-225X",
doi="10.22034/aot.1610.1035",
url="http://www.aot-math.org/article_38442.html"
}
@Article{Chmielinski2016,
author="Chmielinski, Jacek",
title="Operators reversing orthogonality in normed spaces",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="1",
pages="8-14",
abstract="We consider linear operators $T\colon X\to X$ on a normed space $X$ which reverse orthogonality, i.e., satisfy the condition$$x\bot y\quad \Longrightarrow\quad Ty\bot Tx,\qquad x,y\in X,$$where $\bot$ stands for Birkhoff orthogonality.",
issn="2538-225X",
doi="10.22034/aot.1610.1021",
url="http://www.aot-math.org/article_38478.html"
}
@Article{Dragomir2016,
author="Dragomir, Sever",
title="Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="1",
pages="15-91",
abstract="In this paper, we survey some recent trace inequalities for operators inHilbert spaces that are connected to Schwarz's, Buzano's and Kato'sinequalities and the reverses of Schwarz inequality known in the literatureas Cassels' inequality and Shisha--Mond's inequality. Applications for somefunctionals that are naturally associated to some of these inequalities andfor functions of operators defined by power series are given. Examples forfundamental functions such as the power, logarithmic, resolvent andexponential functions are provided as well.",
issn="2538-225X",
doi="10.22034/aot.1610.1032",
url="http://www.aot-math.org/article_38906.html"
}
@Article{Kadelburg2016,
author="Kadelburg, Zoran
and Nastasi, Antonella
and Radenovic, Stojan
and Vetro, Pasquale",
title="Fixed points of contractions and cyclic contractions on $C^{*}$-algebra-valued $b$-metric spaces",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="1",
pages="92-103",
abstract="In this paper, we discuss and improve some recent results aboutcontractive and cyclic mappings established in the framework of$C^{*}$-algebra-valued $b$-metric spaces. Our proofs are muchshorter than the ones in existing literature. Also, we give twoexamples that support our approach.",
issn="2538-225X",
doi="10.22034/aot.1610.1030",
url="http://www.aot-math.org/article_38953.html"
}
@Article{Krnic2016,
author="Krnic, Mario
and Mikic, Rozarija
and Pecaric, Josip",
title="Strengthened converses of the Jensen and Edmundson-Lah-Ribaric inequalities",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="1",
pages="104-122",
abstract="In this paper, we give converses of the Jensen and Edmundson-Lah-Ribaric inequalities which are more accurate than the existing ones. These converses are given in a difference form and they rely on the recent refinement of the Jensen inequality obtained via linear interpolation of a convex function. As an application, we also derive improved converse relations for generalized means, for the Holder and Hermite-Hadamard inequalities as well as for the inequalities of Giaccardi and Petrovic.",
issn="2538-225X",
doi="10.22034/aot.1610.1040",
url="http://www.aot-math.org/article_39602.html"
}
@Article{Tian2016,
author="Tian, Feng
and Jorgensen, Palle",
title="Positive definite kernels and boundary spaces",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="1",
pages="123-133",
abstract="We consider a kernel based harmonic analysis of "boundary,"and boundary representations. Our setting is general: certain classesof positive definite kernels. Our theorems extend (and are motivatedby) results and notions from classical harmonic analysis on the disk.Our positive definite kernels include those defined on infinite discretesets, for example sets of vertices in electrical networks, or discretesets which arise from sampling operations performed on positive definitekernels in a continuous setting. Below we give a summary of main conclusions in the paper: Startingwith a given positive definite kernel $K$ we make precise generalizedboundaries for $K$. They are measure theoretic "boundaries."Using the theory of Gaussian processes, we show that there is alwayssuch a generalized boundary for any positive definite kernel.",
issn="2538-225X",
doi="10.22034/aot.1610.1044",
url="http://www.aot-math.org/article_40547.html"
}
@Article{Aral2016,
author="Aral, Ali
and Gupta, Vijay",
title="(p,q)-type beta functions of second kind",
journal="Advances in Operator Theory",
year="2016",
volume="1",
number="1",
pages="134-146",
abstract="In the present article, we propose the (p,q)-variant of beta function of second kind and establish a relation between the generalized beta and gamma functions using some identities of the post-quantum calculus. As an application, we also propose the (p,q)-Baskakov-Durrmeyer operators, estimate moments and establish some direct results.",
issn="2538-225X",
doi="10.22034/aot.1609.1011",
url="http://www.aot-math.org/article_40548.html"
}