Banach spaces with a basis that are hereditarily asymptotically isometric to l 1 and the fixed point property

We show that there is an equivalent norm in a Banach space with a basis which is hereditarily asymptotically isometric to l 1 such that every subspace has in turn a subspace with the fixed point property. Also we give an example of a family of non-reflexive spaces not isomorphic to l 1 having the fi...

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Bibliographic Details
Published inNonlinear analysis Vol. 71; no. 10; pp. 4598 - 4608
Main Authors Fetter, Helga, Gamboa de Buen, Berta
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 2009
Subjects
Asymptotically isometrically [formula omitted]
Fixed point property
Asymptotically isometrically l 1
Fixed point property
primary
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Summary:We show that there is an equivalent norm in a Banach space with a basis which is hereditarily asymptotically isometric to l 1 such that every subspace has in turn a subspace with the fixed point property. Also we give an example of a family of non-reflexive spaces not isomorphic to l 1 having the fixed point property and other related examples.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2009.03.024