eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
1
1
7
10.22034/aot.1610.1035
38442
Square inequality and strong order relation
Tsuyoshi Ando
ando@es.hokudai.ac.jp
1
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.
http://www.aot-math.org/article_38442_d9989f3fd74949a9277c13928345bcef.pdf
Square inequality
strong order relation
operator arithmetic-geometric mean inequality
Kantorovich constant
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
1
8
14
10.22034/aot.1610.1021
38478
Operators reversing orthogonality in normed spaces
Jacek Chmielinski
jacek@up.krakow.pl
1
Pedagogical University of Cracow
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.
http://www.aot-math.org/article_38478_7c15ca13cf82bd7c234123b9bb787e61.pdf
Birkhoff orthogonality
orthogonality preserving mappings
orthogonality reversing map-pings
linear similarities
characterizations of inner product spaces
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
1
15
91
10.22034/aot.1610.1032
38906
Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces
Sever Dragomir
sever.dragomir@vu.edu.au
1
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.
http://www.aot-math.org/article_38906_2284ce53f9a52e67a0bd59db77882ece.pdf
Trace class operators
Hilbert-Schmidt operators
Trace
Schwarz inequality
Kato inequality
Cassels inequality
Shisha--Mond inequality
Trace inequalities for matrices
Power series of operators
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
1
92
103
10.22034/aot.1610.1030
38953
Fixed points of contractions and cyclic contractions on $C^{*}$-algebra-valued $b$-metric spaces
Zoran Kadelburg
kadelbur@matf.bg.ac.rs
1
Antonella Nastasi
ella.nastasi.93@gmail.com
2
Stojan Radenovic
radens@beotel.rs
3
Pasquale Vetro
pasquale.vetro@unipa.it
4
Department of Mathematics and Computer Science, University of Palermo
Faculty of Mechanical Engineering, University of Belgrade
Department of Mathematics and Computer Science, University of Palermo
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.
http://www.aot-math.org/article_38953_c05393d482953043bf82592dbe9115d3.pdf
$C^{*}$-algebra-valued $b$-metric space
$b$-metric space
cyclic type mapping
expansive mapping
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
1
104
122
10.22034/aot.1610.1040
39602
Strengthened converses of the Jensen and Edmundson-Lah-Ribaric inequalities
Mario Krnic
mario.krnic@fer.hr
1
Rozarija Mikic
jaksic.rozarija@gmail.com
2
Josip Pecaric
pecaric@element.hr
3
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.
http://www.aot-math.org/article_39602_68b5a4686f6f70886b4597b3324fecf9.pdf
positive linear functional
convex function
converse
Jensen inequality
Edmundson-Lah-Ribaric inequality
Holder inequality
Hermite-Hadamard inequality
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
1
123
133
10.22034/aot.1610.1044
40547
Positive definite kernels and boundary spaces
Feng Tian
james.ftian@gmail.com
1
Palle Jorgensen
palle-jorgensen@uiowa.edu
2
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.
http://www.aot-math.org/article_40547_eff3ba46ba5c59cdb0769db9b537f59e.pdf
Gaussian free fields
reproducing kernel Hilbert space
discrete analysis
Green's function
non-uniform sampling
eng
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2538-225X
2016-12-01
1
1
134
146
10.22034/aot.1609.1011
40548
(p,q)-type beta functions of second kind
Ali Aral
aliaral73@yahoo.com
1
Vijay Gupta
vijaygupta2001@hotmail.com
2
No
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.
http://www.aot-math.org/article_40548_62e3853082d62ca9f3f5adb1dcc194c2.pdf
(p,q)-beta function of second kind, (p
q)-gamma function, Baskakov operator, Durrmeyer variant