On a problem of H. P. Rosenthal
type: Item
instance of: scholarly article
zbMATH Open document ID: 0987.46016
author: Benoît Bossard
publication date: 2001-05-16T00:00:00Z
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 1599058
zbMATH Keywords: non-reflexive separable Banach space
zbMATH Keywords: ordinal index
zbMATH Keywords: bidual
zbMATH Keywords: isomorph of \(c_0\)
MaRDI profile type: Publication
title: On a problem of H. P. Rosenthal
published in: Houston Journal of Mathematics
review text: H. P. Rosenthal associated with a non-reflexive separable Banach space \(X\) an ordinal index defined on the elements of the bidual, and shows that \(X\) contains no isomorph of \(c_0\) iff for any element of the bidual which is not in the space the value of the index is countable. Here, it is shown that if \(X\) contains no isomorph of \(c_0\), then in some cases the ordinal index is uniformly bounded on the elements of the bidual which are not in the space by a countable ordinal. In particular, it is true when \(X\) contains no isomorph of \(\ell_1\).
reviewed by: Joe Howard
description: scientific article; zbMATH DE number 1599058