Isomorphic embeddings and harmonic behaviour of smooth operators
type: Item
instance of: scholarly article
title: Isomorphic embeddings and harmonic behaviour of smooth operators
zbMATH Open document ID: 1076.46003
DOI: 10.1007/BF02803504
author: Petr Hájek
author: Michal Johanis
published in: Israel Journal of Mathematics
publication date: 2005-03-07T00:00:00Z
review text: Conditions for embeddings \(\ell^p\) and \(c_0\) into a Banach space \(Y\) are given. Namely, if \(c_0^+\subset Y\) then \(c_0\subset Y\). Let \(1<p<\infty\). If \(\ell^p_+\subset Y\) then \(\ell^p\subset Y\). This result is applied to the study of highly smooth operators from \(\ell^p\) into~\(Y\) (\(p/2\notin {\mathbb N}\)). Let \(Y\) be a Banach space, \(1\leqslant p<\infty\), \(p/2\notin {\mathbb N}\) and let \(C=C^{[p],\alpha}(B_{\ell^p},Y)\) for some \(1\geqslant \alpha >p-[p]\) if \(p\notin {\mathbb N}\), or \(C=C^{p,+} (B_{\ell^p},Y)\) if \(p\) is an odd integer. Then either all operators in~\(C\) have a harmonic behaviour or \(\ell^{p/k}\subset Y\) for some \(1\leqslant k\leqslant [p]\).
Mathematics Subject Classification ID: 46B03
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 2141379
zbMATH Keywords: isomorphic embedding
zbMATH Keywords: Banach space
zbMATH Keywords: smooth operator
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02803504
OpenAlex ID: W2061107129
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description: scientific article; zbMATH DE number 2141379