ORIGINAL_ARTICLE
Square inequality and strong order relation
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
2016-12-01T11:23:20
2018-03-19T11:23:20
1
7
10.22034/aot.1610.1035
Square inequality
strong order relation
operator arithmetic-geometric mean inequality
Kantorovich constant
Tsuyoshi
Ando
ando@es.hokudai.ac.jp
true
1
LEAD_AUTHOR
ORIGINAL_ARTICLE
Operators reversing orthogonality in normed spaces
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.
http://www.aot-math.org/article_38478_7c15ca13cf82bd7c234123b9bb787e61.pdf
2016-12-01T11:23:20
2018-03-19T11:23:20
8
14
10.22034/aot.1610.1021
Birkhoff orthogonality
orthogonality preserving mappings
orthogonality reversing map-pings
linear similarities
characterizations of inner product spaces
Jacek
Chmielinski
jacek@up.krakow.pl
true
1
Pedagogical University of Cracow
Pedagogical University of Cracow
Pedagogical University of Cracow
LEAD_AUTHOR
ORIGINAL_ARTICLE
Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces
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
2016-12-01T11:23:20
2018-03-19T11:23:20
15
91
10.22034/aot.1610.1032
trace class operators
Hilbert-Schmidt operators
Trace
Schwarz inequality
Kato inequality
Cassels inequality
Shisha--Mond inequality
Trace inequalities for matrices
Power series of operators
Sever
Dragomir
sever.dragomir@vu.edu.au
true
1
LEAD_AUTHOR
ORIGINAL_ARTICLE
Fixed points of contractions and cyclic contractions on $C^{*}$-algebra-valued $b$-metric spaces
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
2016-12-01T11:23:20
2018-03-19T11:23:20
92
103
10.22034/aot.1610.1030
$C^{*}$-algebra-valued $b$-metric space
$b$-metric space
cyclic type mapping
expansive mapping
Zoran
Kadelburg
kadelbur@matf.bg.ac.rs
true
1
LEAD_AUTHOR
Antonella
Nastasi
ella.nastasi.93@gmail.com
true
2
Department of Mathematics and Computer Science,
University of Palermo
Department of Mathematics and Computer Science,
University of Palermo
Department of Mathematics and Computer Science,
University of Palermo
AUTHOR
Stojan
Radenovic
radens@beotel.rs
true
3
Faculty of Mechanical Engineering, University of Belgrade
Faculty of Mechanical Engineering, University of Belgrade
Faculty of Mechanical Engineering, University of Belgrade
AUTHOR
Pasquale
Vetro
pasquale.vetro@unipa.it
true
4
Department of Mathematics and Computer Science,
University of Palermo
Department of Mathematics and Computer Science,
University of Palermo
Department of Mathematics and Computer Science,
University of Palermo
AUTHOR
ORIGINAL_ARTICLE
Strengthened converses of the Jensen and Edmundson-Lah-Ribaric inequalities
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
2016-12-01T11:23:20
2018-03-19T11:23:20
104
122
10.22034/aot.1610.1040
positive linear functional
convex function
converse
Jensen inequality
Edmundson-Lah-Ribaric inequality
Holder inequality
Hermite-Hadamard inequality
Mario
Krnic
mario.krnic@fer.hr
true
1
LEAD_AUTHOR
Rozarija
Mikic
jaksic.rozarija@gmail.com
true
2
AUTHOR
Josip
Pecaric
pecaric@element.hr
true
3
AUTHOR
ORIGINAL_ARTICLE
Positive definite kernels and boundary spaces
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
2016-12-01T11:23:20
2018-03-19T11:23:20
123
133
10.22034/aot.1610.1044
Gaussian free fields
reproducing kernel Hilbert space
discrete analysis
Green's function
non-uniform sampling
Feng
Tian
james.ftian@gmail.com
true
1
LEAD_AUTHOR
Palle
Jorgensen
palle-jorgensen@uiowa.edu
true
2
AUTHOR
ORIGINAL_ARTICLE
(p,q)-type beta functions of second kind
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
2016-12-01T11:23:20
2018-03-19T11:23:20
134
146
10.22034/aot.1609.1011
(p,q)-beta function of second kind, (p
q)-gamma function, Baskakov operator, Durrmeyer variant
Ali
Aral
aliaral73@yahoo.com
true
1
LEAD_AUTHOR
Vijay
Gupta
vijaygupta2001@hotmail.com
true
2
No
No
No
AUTHOR