An extension of a result of Ribe
type: Item
instance of: scholarly article
title: An extension of a result of Ribe
zbMATH Open document ID: 0613.46025
DOI: 10.1007/BF02776080
author: Israel Aharoni
author: J. Lindenstrauss
published in: Israel Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: If \(1<q<\infty\), \(1<p_ n<\infty\) and \(p_ n\to 1\) then \textit{M. Ribe} [Isr. J. Math. 48, 139-147 (1984; Zbl 0577.46015)] proved that the Banach spaces \(X=(\Sigma \oplus L_{p_ n})_ q\) and \(X\oplus L_ 1\) are uniformly homeomorphic but not Lipschitz equivalent. One of the results of the present paper shows that if \(1\leq p<\infty\), \(1\leq p_ n<\infty\), \(p_ n\to p\), \(1\leq q<\infty\), then \(X=(\Sigma \oplus \ell_{p_ n})_ q\) is uniformly homeomorphic to \(Y=X\oplus \ell_ p\), while if \(p_ n\neq p\), \(q\neq p\), Y is not Lipschitz homeomorphic to any subset of X.
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 3992169
zbMATH Keywords: uniformly homeomorphic but not Lipschitz equivalent
MaRDI profile type: Publication
cites work: On the differentiability of Lipschitz mappings in Fréchet spaces
cites work: The homotopy structure of the linear group of a Banach space
cites work: Existence of separable uniformly homeomorphic nonisomorphic Banach spaces
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description: scientific article; zbMATH DE number 3992169