Square inequality and strong order relation
Tsuyoshi
Ando
author
text
article
2016
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
1
no.
2016
1
7
http://www.aot-math.org/article_38442_d9989f3fd74949a9277c13928345bcef.pdf
dx.doi.org/10.22034/aot.1610.1035
Operators reversing orthogonality in normed spaces
Jacek
Chmielinski
Pedagogical University of Cracow
author
text
article
2016
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
1
no.
2016
8
14
http://www.aot-math.org/article_38478_7c15ca13cf82bd7c234123b9bb787e61.pdf
dx.doi.org/10.22034/aot.1610.1021
Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces
Sever
Dragomir
author
text
article
2016
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
1
no.
2016
15
91
http://www.aot-math.org/article_38906_2284ce53f9a52e67a0bd59db77882ece.pdf
dx.doi.org/10.22034/aot.1610.1032
Fixed points of contractions and cyclic contractions on $C^{*}$-algebra-valued $b$-metric spaces
Zoran
Kadelburg
author
Antonella
Nastasi
Department of Mathematics and Computer Science,
University of Palermo
author
Stojan
Radenovic
Faculty of Mechanical Engineering, University of Belgrade
author
Pasquale
Vetro
Department of Mathematics and Computer Science,
University of Palermo
author
text
article
2016
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
1
no.
2016
92
103
http://www.aot-math.org/article_38953_c05393d482953043bf82592dbe9115d3.pdf
dx.doi.org/10.22034/aot.1610.1030
Strengthened converses of the Jensen and Edmundson-Lah-Ribaric inequalities
Mario
Krnic
author
Rozarija
Mikic
author
Josip
Pecaric
author
text
article
2016
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
1
no.
2016
104
122
http://www.aot-math.org/article_39602_68b5a4686f6f70886b4597b3324fecf9.pdf
dx.doi.org/10.22034/aot.1610.1040
Positive definite kernels and boundary spaces
Feng
Tian
author
Palle
Jorgensen
author
text
article
2016
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
1
no.
2016
123
133
http://www.aot-math.org/article_40547_eff3ba46ba5c59cdb0769db9b537f59e.pdf
dx.doi.org/10.22034/aot.1610.1044
(p,q)-type beta functions of second kind
Ali
Aral
author
Vijay
Gupta
No
author
text
article
2016
eng
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.
Advances in Operator Theory
Tusi Mathematical Research Group (TMRG)
2538-225X
1
v.
1
no.
2016
134
146
http://www.aot-math.org/article_40548_62e3853082d62ca9f3f5adb1dcc194c2.pdf
dx.doi.org/10.22034/aot.1609.1011