Renormings and the fixed point property in non-commutative L sub(1)-spaces

Let [inline image] be a finite von Neumann algebra. It is known that [inline image] and every non-reflexive subspace of [inline image] fail to have the fixed point property for non-expansive mappings (FPP). We prove a new fixed point theorem for this class of mappings in non-commutative [inline imag...

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Bibliographic Details
Published in:Nonlinear analysis 2011-07, Vol.74 (10), p.3091-3098
Main Authors: Hernandez-Linares, Carlos A, Japon, Maria A
Format: Article
Language:English
Subjects:
Algebra
Banach space
Fixed points (mathematics)
Mapping
Mathematical analysis
Nonlinearity
Subspaces
Theorems
Online Access:Get full text
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Summary:Let [inline image] be a finite von Neumann algebra. It is known that [inline image] and every non-reflexive subspace of [inline image] fail to have the fixed point property for non-expansive mappings (FPP). We prove a new fixed point theorem for this class of mappings in non-commutative [inline image] Banach spaces which lets us obtain a sufficient condition such that a closed subspace of [inline image] can be renormed to satisfy the FPP. As a consequence, we deduce that the predual of every atomic finite von Neumann algebra can be renormed with the FPP.
ISSN:0362-546X
DOI:10.1016/j.na.2011.01.022