Factorization through Lorentz spaces for operators acting in Banach function spaces

We show a factorization through Lorentz spaces for Banach-space-valued operators defined in Banach function spaces. Although our results are inspired in the classical factorization theorem for operators from L s -spaces through Lorentz spaces L q , 1 due to Pisier, our arguments are different and es...

Full description

Saved in:
Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2019-02, Vol.23 (1), p.75-88
Main Author: Sánchez Pérez, E. A.
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Econometrics
Factorization
Fourier Analysis
Function space
Mathematics
Mathematics and Statistics
Operator Theory
Operators
Potential Theory
Theorems
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We show a factorization through Lorentz spaces for Banach-space-valued operators defined in Banach function spaces. Although our results are inspired in the classical factorization theorem for operators from L s -spaces through Lorentz spaces L q , 1 due to Pisier, our arguments are different and essentially connected with Maurey’s theorem for operators that factor through L p -spaces. As a consequence, we obtain a new characterization of Lorentz L q , 1 -spaces in terms of lattice geometric properties, in the line of the (isomorphic) description of L p -spaces as the unique ones that are p -convex and p -concave.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-018-0593-2