On subspaces and quotients of Banach spaces \(C(K,X)\)
type: Item
instance of: scholarly article
title: On subspaces and quotients of Banach spaces \(C(K,X)\)
zbMATH Open document ID: 1044.46034
author: Elói M. Galego
published in: Monatshefte für Mathematik
publication date: 2002-09-10T00:00:00Z
review text: Let \(C(K,X)\) denote the continuous vector-valued functions on a dispersed compact set \(K\). It is proved that every infinite-dimensional closed subspace of \(C(K,X)\) that is totally incomparable to \(X\) contains a complemented subspace isomorphic to \(c\). It is also shown that complemented subspaces that fail to contain \(c\) are isomorphic to a complemented subspace of a direct sum of finitely many copies of \(X\), and that the same is true with ``complemented'' replaced by ``quotient''. Other geometric properties of these spaces \(C(K,X)\) are also given.
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46B03
zbMATH DE Number: 1798909
reviewed by: James R. Holub
MaRDI profile type: Publication
full work available at URL: s006050200036
OpenAlex ID: W2008388429
DOI: 10.1007/S006050200036
description: scientific article; zbMATH DE number 1798909