A note on norm-one projections onto subspaces of finite codimension of \(l^{\infty}\)
type: Item
instance of: scholarly article
title: A note on norm-one projections onto subspaces of finite codimension of \(l^{\infty}\)
zbMATH Open document ID: 0682.46014
DOI: 10.1007/BF01189587
author: Marco Baronti
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: Let X be a real linear normed space and let \(Y\subset X\) be a closed subspace. An operator P: \(X\to Y\) is a projection if P is linear, continuous and such that \(Py=y\) for any y in Y. A projection P is said to be: 1) strictly contractive if \(\| Px\| <\| x\|\) for any \(x\not\in Y,\) 2) bicontractive if \(\| P\| =\| I-P\| =1.\) In this paper we prove that in \(\ell^{\infty}\) no subspace of finite codimension is the range of a strictly contractive projection and moreover we characterize the hyperplanes which are the range of a bicontractive projection. Some references about projections are in \textit{M. Baronti} and \textit{P. L. Papini} [Ann. Mat. Pura Appl. 4, 53-61 (1988)], \textit{B. Beauzamy} [Bull. Sci. Math. 102, 43-47 (1978; Zbl 0376.46011)].
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 4117215
zbMATH Keywords: strictly contractive projection
zbMATH Keywords: bicontractive projection
MaRDI profile type: Publication
cites work: Norm-one projections onto subspaces of \(\ell _ p\)
cites work: Norm-one projections onto subspaces of \((\ell ^{\infty})\)
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cites work: Q4153188
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description: scientific article; zbMATH DE number 4117215