On CL-spaces and almost CL-spaces
type: Item
instance of: scholarly article
title: On CL-spaces and almost CL-spaces
zbMATH Open document ID: 1057.46020
DOI: 10.1007/BF02432912
author: Miguel Martín
author: Rafael Payá
published in: Arkiv för Matematik
publication date: 2004-09-28T00:00:00Z
review text: A complex Banach space \(X\) is said to be a \(CL\)-space (almost CL-space) if for every maximal face \(F\) of the unit sphere, the unit ball is the (norm closed) absolute convex hull of \(F\). These concepts were studied earlier by \textit{Å. Lima} [Ann. Inst. Fourier 28, No. 3, 35--65 (1978; Zbl 0347.46018)]. This paper contributes mainly to the study of complex CL (almost CL) spaces. Newer examples of spaces satisfying these properties are generated by considering direct sums and spaces of vector-valued continuous functions. For example, these properties are preserved by \(c_0\)-direct sums, but only by finite \(\ell^1\)-direct sums. In the case of \(C(K,X)\), the space of vector-valued continuous functions on a compact set \(K\), \(C(K,X)\) is an almost CL-space if and only if \(X\) is, and if \(C(K,X)\) is a CL-space, then so is \(X\).
reviewed by: T.S.S.R.K. Rao
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46E40
zbMATH DE Number: 2103841
zbMATH Keywords: maximal face
zbMATH Keywords: CL-space
zbMATH Keywords: almost CL-space
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02432912
OpenAlex ID: W2014634473
description: scientific article; zbMATH DE number 2103841