Banach spaces of vector-valued functions
type: Item
instance of: scholarly article
title: Banach spaces of vector-valued functions
zbMATH Open document ID: 0902.46017
author: Pilar Cembranos
author: José Mendoza
published in: Lecture Notes in Mathematics
publication date: 1997-12-10T00:00:00Z
review text: This small monograph is devoted to the classical problems of geometry of Banach spaces about the existence of copies and complemented copies of \(c_0\), \(\ell_1\) and \(\ell_\infty\) in Banach vector-function spaces \(L_p(\mu,X)\) \((1\leq p\leq\infty)\) and \({\mathcal C}(K,X)\) (here \(X\) is a Banach space) under different assumptions about \(\mu\) and \(K\). The authors present an exhausting and systematical summary of all, known to this time, results in this field (in particular, results by S. Kwapień, G. Pisier, E. Saab -- P. Saab, C. Cembranos, F. Freniche, L. Drewnowski, F. Bombal, G. Emmanuelle, J. Mendoza, D. Leuing -- F. Räbiger, S. Díaz, N. J. Kalton and others) and formulate some unsolved problems. In particular, the authors describe all situations when the existence of copies or complemented copies of \(c_0\), \(\ell_1\) and \(\ell_\infty\) in spaces \(L_p(\mu, X)\) \((1\leq p\leq\infty)\) and in \({\mathcal C}(K, X)\) is turned out to be equivalent to their existence in the spaces \(X\) or \(L_p(\mu)\) and \({\mathcal C}(K)\) correspondingly. The book is written in laconic and clear manner. It can be considered as a good supplement to the classical books in the field of J. Diestel, J. Diestel and J. J. Uhl. Undoubtedly, this book will be useful for all specialists in the field.
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46-02
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 1095902
zbMATH Keywords: geometry of Banach spaces
zbMATH Keywords: complemented copies
zbMATH Keywords: Banach vector-function spaces
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0096765
OpenAlex ID: W597268295
DOI: 10.1007/BFB0096765
description: scientific article; zbMATH DE number 1095902