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 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.

scholarly journals Operators on Injective Banach Lattices

2016 ◽  
Author(s):  
A.G. Kusraev
Keyword(s):  
Banach Lattice ◽  
Linear Operators ◽  
Banach Lattices ◽  
Transfer Principle ◽  
Bounded Linear Operators ◽  
Bounded Linear

The paper deals with some properties of bounded linear operators on injective Banach lattice using a Boolean-valued transfer principle from AL-spaces to injectives stated in author's previous work.

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 An Extension of Nikishin’s Factorization Theorem

2017 ◽  
Vol 60 (1) ◽  
pp. 104-110
Author(s):  
Geoff Diestel
Keyword(s):  
Weak Type ◽  
Factorization Theorem ◽  
Multilinear Operators ◽  
Lebesgue Spaces

AbstractA Nikishin–Maurey characterization is given for bounded subsets of weak-type Lebesgue spaces. New factorizations for linear and multilinear operators are shown to follow.

Spectral and asymptotic properties of resolvent-dominated operators

2000 ◽  
Vol 68 (2) ◽  
pp. 181-201 ◽  
Author(s):  
Frank Räbiger ◽  
Manfred P. H. Wolff
Keyword(s):  
Banach Lattice ◽  
Asymptotic Properties ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear

AbstractLet A and B be (not necessarily bounded) linear operators on a Banach lattice E such that |(s – B)-1x|≤ (s – A)-1|x| for all x in E and sufficiently large s ∈ R. The main purpose of this paper is to investigate the relation between the spectra σ(B) and σ(A) of B and A, respectively. We apply our results to study asymptotic properties of dominated C0-semigroups.

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.

scholarly journals The iterates of positive linear operators with the set of constant functions as the fixed point set

2016 ◽  
Vol 32 (2) ◽  
pp. 165-172
Author(s):  
TEODORA CATINAS ◽  
◽  
DIANA OTROCOL ◽  
IOAN A. RUS ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Linear Operator ◽  
Banach Lattice ◽  
Nonempty Subset ◽  
Positive Linear Operator ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Fixed Point Set ◽  
Real Functions ◽  
Point Set

Let Ω ⊂ Rp, p ∈ N∗ be a nonempty subset and B(Ω) be the Banach lattice of all bounded real functions on Ω, equipped with sup norm. Let X ⊂ B(Ω) be a linear sublattice of B(Ω) and A: X → X be a positive linear operator with constant functions as the fixed point set. In this paper, using the weakly Picard operators techniques, we study the iterates of the operator A. Some relevant examples are also given.

Korovkin Theorems for Integral Operators with Kernels of Finite Oscillation

1974 ◽  
Vol 26 (6) ◽  
pp. 1390-1404 ◽  
Author(s):  
M. J. Marsden ◽  
S. D. Riemenschneider
Keyword(s):  
Banach Space ◽  
Banach Lattice ◽  
Measure Space ◽  
Integral Operators ◽  
Finite Measure ◽  
Bounded Sequence ◽  
Positive Operators ◽  
Linear Operators ◽  
Finite Measure Space

There has been considerable interest recently in the investigation of "Korovkin sets". Briefly, for X a Banach space and a family of linear operators on X, a subset K ⊂ X is a Korovkin set relative to if for any bounded sequence {Tn} ⊂ , Tnk → k in X for each k ∊ K implies Tnx → x for each x ∊ X. A large portion of these investigations have been carried out for X being one of the spaces C(S), S compact Hausdorff, the usual Lp spaces of functions on some finite measure space, or some Banach lattice; while is one of the classes +-positive operators, 1-contractions (i.e., ||T|| 1), or + ⋂1

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