On Pitt's theorem for operators between scalar and vector-valued quasi-Banach sequence spaces
type: Item
instance of: scholarly article
title: On Pitt's theorem for operators between scalar and vector-valued quasi-Banach sequence spaces
zbMATH Open document ID: 0995.46016
author: Andreas Defant
author: J. A. López Molina
author: M. J. Rivera
published in: Monatshefte für Mathematik
publication date: 2000-06-27T00:00:00Z
review text: This article presents extensions of the classical theorem of Pitt about the compactness of all operators from \(\ell_p\) into \(\ell_q\) if \(p> q\) to a wide class of quasi-Banach sequence spaces. Applications are given to quasi-normed Minkowski, Lorentz and Orlicz sequence spaces. The proofs are based on gliding hump methods. The case of Banach spaces of vector valued sequences is also treated. Several results are improved in the last section by use of an extension of the Maurey-Rosenthal factorization theory for operators between Banach sequence spaces, thus showing that the compact operators in fact factorize through suitable \(\ell_p\)-spaces.
reviewed by: José Bonet
Mathematics Subject Classification ID: 46B45
Mathematics Subject Classification ID: 46A32
Mathematics Subject Classification ID: 46M05
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 46A16
Mathematics Subject Classification ID: 46B07
zbMATH DE Number: 1466223
zbMATH Keywords: quasi-Banach sequence spaces
zbMATH Keywords: quasi-normed Minkowski, Lorentz and Orlicz sequence spaces
zbMATH Keywords: gliding hump methods
zbMATH Keywords: Maurey-Rosenthal factorization theory
MaRDI profile type: Publication
full work available at URL: s006050050083
OpenAlex ID: W2080355090
DOI: 10.1007/S006050050083
description: scientific article; zbMATH DE number 1466223