scholarly journals On the Composition Ideals of Schatten Class Type Mappings

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Abdelaziz Belaada ◽  
Khalil Saadi ◽  
Abdelmoumen Tiaiba
Keyword(s):  
Linear Operators ◽  
Multilinear Operators ◽  
Schatten Classes ◽  
Schatten Class ◽  
Polynomial Mappings ◽  
Coincidence Theorems

We study the composition ideals of multilinear and polynomial mappings generated by Schatten classes. We give some coincidence theorems for Cohen strongly 2-summing multilinear operators and factorization results like that given by Lindenstrauss-Pełczński for Hilbert Schmidt linear operators.

scholarly journals Pietsch’s variants of s-numbers for multilinear operators

2021 ◽  
Vol 115 (4) ◽  
Author(s):  
D. L. Fernandez ◽  
M. Mastyło ◽  
E. B. Silva
Keyword(s):  
Linear Operator ◽  
Linear Operators ◽  
Multilinear Operators ◽  
Dual Operator ◽  
Range Space ◽  
Linear Forms ◽  
Fundamental Properties

AbstractWe study variants of s-numbers in the context of multilinear operators. The notion of an $$s^{(k)}$$ s ( k ) -scale of k-linear operators is defined. In particular, we shall deal with multilinear variants of the $$s^{(k)}$$ s ( k ) -scales of the approximation, Gelfand, Hilbert, Kolmogorov and Weyl numbers. We investigate whether the fundamental properties of important s-numbers of linear operators are inherited to the multilinear case. We prove relationships among some $$s^{(k)}$$ s ( k ) -numbers of k-linear operators with their corresponding classical Pietsch’s s-numbers of a generalized Banach dual operator, from the Banach dual of the range space to the space of k-linear forms, on the product of the domain spaces of a given k-linear operator.

Random Euclidean sections of some classical Banach spaces

2002 ◽  
Vol 91 (2) ◽  
pp. 247 ◽  
Author(s):  
Y. Gordon ◽  
O. Guédon ◽  
M. Meyer ◽  
A. Pajor
Keyword(s):  
Euclidean Space ◽  
Banach Spaces ◽  
Normed Space ◽  
Linear Operators ◽  
Schatten Classes ◽  
Random Subspaces

Using probabilistic arguments, we give precise estimates of the Banach-Mazur distance of subspaces of the classical $\ell_q^n$ spaces and of Schatten classes of operators $S_q^n$ for $q \ge 2$ to the Euclidean space. We also estimate volume ratios of random subspaces of a normed space with respect to subspaces of quotients of $\ell_q$. Finally, the preceeding methods are applied to give estimates of Gelfand numbers of some linear operators.

scholarly journals Domination and Kwapień’s factorization theorems for positive Cohen p–nuclear m–linear operators

2021 ◽  
Vol 7 (1) ◽  
pp. 100-115
Author(s):  
Amar Bougoutaia ◽  
Amar Belacel ◽  
Halima Hamdi
Keyword(s):  
Banach Lattice ◽  
Linear Operators ◽  
Factorization Theorem ◽  
Multilinear Operators ◽  
Natural Analog ◽  
Pietsch Domination Theorem

AbstractIn this paper, we introduce and study the concept of positive Cohen p-nuclear multilinear operators between Banach lattice spaces. We prove a natural analog to the Pietsch domination theorem for this class. Moreover, we give like the Kwapień’s factorization theorem. Finally, we investigate some relations with another known classes.

scholarly journals Spectrality of elementary operators

1990 ◽  
Vol 49 (2) ◽  
pp. 327-346 ◽  
Author(s):  
Milan Hladnik
Keyword(s):  
Complete Characterization ◽  
Linear Operators ◽  
Schatten Classes ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Von Neumann ◽  
Infinite Dimensional ◽  
Normal Operators ◽  
Elementary Operators

AbstractSpectrality and prespectrality of elementary operators , acting on the algebra B(k) of all bounded linear operators on a separable infinite-dimensional complex Hubert space K, or on von Neumann-Schatten classes in B(k), are treated. In the case when (a1, a2, …, an) and (b1, b2, …, bn) are two n—tuples of commuting normal operators on H, the complete characterization of spectrality is given.

scholarly journals Schatten class and Berezin transform of quaternionic linear operators

2016 ◽  
Vol 39 (18) ◽  
pp. 5582-5606 ◽  
Author(s):  
Fabrizio Colombo ◽  
Jonathan Gantner ◽  
Tim Janssens
Keyword(s):  
Berezin Transform ◽  
Linear Operators ◽  
Schatten Class

scholarly journals Isomorphisms from the Space of Multilinear Operators

2019 ◽  
Vol 27 (2) ◽  
pp. 101-106
Author(s):  
Kazuhisa Nakasho
Keyword(s):  
Linear Operators ◽  
Multilinear Operators ◽  
Normed Spaces ◽  
Bilinear Operators

Summary In this article, using the Mizar system [5], [2], the isomorphisms from the space of multilinear operators are discussed. In the first chapter, two isomorphisms are formalized. The former isomorphism shows the correspondence between the space of multilinear operators and the space of bilinear operators. The latter shows the correspondence between the space of multilinear operators and the space of the composition of linear operators. In the last chapter, the above isomorphisms are extended to isometric mappings between the normed spaces. We referred to [6], [11], [9], [3], [10] in this formalization.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

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