2018-04-22T03:23:11Z
http://www.aot-math.org/?_action=export&rf=summon&issue=4618
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
1
Square inequality and strong order relation
Tsuyoshi
Ando
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.
Square inequality
strong order relation
operator arithmetic-geometric mean inequality
Kantorovich constant
2016
12
01
1
7
http://www.aot-math.org/article_38442_d9989f3fd74949a9277c13928345bcef.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
1
Operators reversing orthogonality in normed spaces
Jacek
Chmielinski
We consider linear operators $Tcolon Xto X$ on a normed space $X$ which reverse orthogonality, i.e., satisfy the condition$$xbot yquad Longrightarrowquad Tybot Tx,qquad x,yin X,$$where $bot$ stands for Birkhoff orthogonality.
Birkhoff orthogonality
orthogonality preserving mappings
orthogonality reversing map-pings
linear similarities
characterizations of inner product spaces
2016
12
01
8
14
http://www.aot-math.org/article_38478_7c15ca13cf82bd7c234123b9bb787e61.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
1
Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces
Sever
Dragomir
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.
trace class operators
Hilbert-Schmidt operators
Trace
Schwarz inequality
Kato inequality
Cassels inequality
Shisha--Mond inequality
Trace inequalities for matrices
Power series of operators
2016
12
01
15
91
http://www.aot-math.org/article_38906_2284ce53f9a52e67a0bd59db77882ece.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
1
Fixed points of contractions and cyclic contractions on $C^{*}$-algebra-valued $b$-metric spaces
Zoran
Kadelburg
Antonella
Nastasi
Stojan
Radenovic
Pasquale
Vetro
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.
$C^{*}$-algebra-valued $b$-metric space
$b$-metric space
cyclic type mapping
expansive mapping
2016
12
01
92
103
http://www.aot-math.org/article_38953_c05393d482953043bf82592dbe9115d3.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
1
Strengthened converses of the Jensen and Edmundson-Lah-Ribaric inequalities
Mario
Krnic
Rozarija
Mikic
Josip
Pecaric
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.
positive linear functional
convex function
converse
Jensen inequality
Edmundson-Lah-Ribaric inequality
Holder inequality
Hermite-Hadamard inequality
2016
12
01
104
122
http://www.aot-math.org/article_39602_68b5a4686f6f70886b4597b3324fecf9.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
1
Positive definite kernels and boundary spaces
Feng
Tian
Palle
Jorgensen
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.
Gaussian free fields
reproducing kernel Hilbert space
discrete analysis
Green's function
non-uniform sampling
2016
12
01
123
133
http://www.aot-math.org/article_40547_eff3ba46ba5c59cdb0769db9b537f59e.pdf
Advances in Operator Theory
Adv. Operator Theory (AOT)
2016
1
1
(p,q)-type beta functions of second kind
Ali
Aral
Vijay
Gupta
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.
(p,q)-beta function of second kind, (p
q)-gamma function, Baskakov operator, Durrmeyer variant
2016
12
01
134
146
http://www.aot-math.org/article_40548_62e3853082d62ca9f3f5adb1dcc194c2.pdf