Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
1
2017
01
01
Fixed point results for a new mapping related to mean nonexpansive mappings.
1
16
EN
Torrey
M
Gallagher
Bucknell University
torreymg@gmail.com
10.22034/aot.1610.1029
Mean nonexpansive mappings were first introduced in 2007 by Goebel and Jap'on Pineda and advances have been made by several authors toward understanding their fixed point properties in various contexts. For any given mean nonexpansive mapping of a Banach space, many of the positive results have been derived from knowing that a certain average of some iterates of the mapping is nonexpansive. However, nothing is known about the properties of a mean nonexpansive mapping which has been averaged with the identity. In this paper we prove some fixed point results for a mean nonexpansive mapping which has been composed with a certain average of itself and the identity and we use this study to draw connections to the original mapping.
Mean nonexpansive,fixed point,approximate fixed point sequence,nonexpansive,nonlinear operator
http://www.aot-math.org/article_41045.html
http://www.aot-math.org/article_41045_27716d12e4fd3af59c801d5f1d0da8bf.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
1
2017
01
01
The AHSp is inherited by $E$-summands
17
20
EN
Francisco
Garcia-Pacheco
0000-0001-6208-6071
University of Cadiz
garcia.pacheco@uca.es
10.22034/aot.1610.1033
In this short note we prove that the Approximate Hyperplane Series property (AHSp) is hereditary to $E$-summands via characterizing the $E$-projections.
Projection,complemented,norm-attaining
http://www.aot-math.org/article_41341.html
http://www.aot-math.org/article_41341_8ae82851113663f16fc778ca616ad896.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
1
2017
01
01
Lipschitz properties of convex functions
21
49
EN
Stefan
Cobzas
Babes-Bolyai University,
Department of Mathematics
scobzas@math.ubbcluj.ro
10.22034/aot.1610.1022
The present paper is concerned with Lipschitz properties of convex mappings. One considers the general context of mappings defined on an open convex subset $Omega$ of a locally convex space $X$ and taking values in a locally convex space $Y$ ordered by a normal cone.One proves also equi-Lipschitz properties for pointwise bounded families of continuous convexmappings, provided the source space $X$ is barrelled. Some results on Lipschitz properties of continuous convex functions defined on metrizable topological vector spaces are included as well.The paper has a methodological character - its aim is to show that some geometric properties (monotonicity of the slope, the normality of the seminorms) allow to extend the proofs from the scalar case to the vector one. In this way the proofs become more transparent and natural.
convex function,convex operator,Lipschitz property,normal cone,normed lattice
http://www.aot-math.org/article_41458.html
http://www.aot-math.org/article_41458_5d243e360281e6cdca04379e93e5493c.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
1
2017
01
01
On the generalized free energy inequality
50
58
EN
Natalia
Bebiano
Universidade de Coimbra
bebiano@mat.uc.pt
Joao
da Providencia
providencia@teor.fis.uc.pt
10.22034/aot.1610.1041
The generalized free energy inequality known from statistical mechanics is stated in the finite dimension setting and the maximizing matrix is restored. Our approach uses the maximum-entropy inference principle and numerical range methods.
Maximum-entropy inference,generalized free energy inequality,von Neumann entropy,Numerical Range
http://www.aot-math.org/article_41815.html
http://www.aot-math.org/article_41815_ffcf885093fd1198f9d79f7ef7a5d321.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
1
2017
01
01
Various notions of best approximation property in spaces of Bochner integrable functions
59
77
EN
Tanmoy
Paul
tanmoy@iith.ac.in
10.22034/aot.1611-1052
We show that a separable proximinal subspace of $X$, say $Y$ is strongly proximinal (strongly ball proximinal) if and only if $L_p(I,Y)$ is strongly proximinal (strongly ball proximinal) in $L_p(I,X)$, for $1leq p
$L_p(I,X)$,proximinality,strong proximinality,ball proximinality
http://www.aot-math.org/article_42347.html
http://www.aot-math.org/article_42347_7cee99d7ceb216023ba0f2c19844765c.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
1
2017
01
01
On the numerical radius of a quaternionic normal operator
78
86
EN
Ramesh
Golla
IIT Hyderabad
rameshg@iith.ac.in
10.22034/aot.1611-1060
We prove that for a right linear bounded normal operator on a quaternionic Hilbert space (quaternionic bounded normal operator) the norm and the numerical radius are equal. As a consequence of this result we give a new proof of the known fact that a non zero quaternionic compact normal operator has a non zero right eigenvalue. Using this we give a new proof of the spectral theorem for quaternionic compact normal operators. Finally, we show that every quaternionic compact operator is norm attaining and prove the Lindenstrauss theorem on norm attaining operators, namely, the set of all norm attaining quaternionic operators is norm dense in the space of all bounded quaternionic operators defined between two quaternionic Hilbert spaces.
Quaternionic Hilbert space,compact operator,right eigenvalue,norm attaining operator,Lindenstrauss theorem
http://www.aot-math.org/article_42343.html
http://www.aot-math.org/article_42343_dd5718aee7212ac0fe294739b54abfd4.pdf
Tusi Mathematical Research Group (TMRG)
Advances in Operator Theory
2538-225X
2
1
2017
01
01
Trigonometric polynomials over homogeneous spaces of compact groups
87
97
EN
Arash
Ghaani Farashahi
arash.ghaani.farashahi@univie.ac.at
10.22034/aot.1701-1090
This paper presents a systematic study for trigonometric polynomials over homogeneous spaces of compact groups.Let $H$ be a closed subgroup of a compact group $G$. Using the abstract notion of dual space $widehat{G/H}$, we introduce the space of trigonometric polynomials $mathrm{Trig}(G/H)$ over the compact homogeneous space $G/H$.As an application for harmonic analysis of trigonometric polynomials, we prove that the abstract dual space of anyhomogeneous space of compact groups separates points of the homogeneous space in some sense.
Compact homogeneous space,compact group,dual space,unitary representation,irreducible representation,trigonometric polynomials
http://www.aot-math.org/article_42397.html
http://www.aot-math.org/article_42397_d58b619d8f15c41e6055deefe8ad8abf.pdf