Banach spaces with a basis that are hereditarily asymptotically isometric to l sub(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 sub(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 sub(1) hav...

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Bibliographic Details
Published in:Nonlinear analysis 2009-11, Vol.71 (10), p.4598-4608
Main Authors: Fetter, Helga, De Buen, Berta Gamboa
Format: Article
Language:English
Online Access:Get full text
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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 sub(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 sub(1) having the fixed point property and other related examples.
ISSN:0362-546X
DOI:10.1016/j.na.2009.03.024