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Proceedings of the American Mathematical Society

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Stability of the fixed point property
of Hilbert spaces


Author: Pei-Kee Lin
Journal: Proc. Amer. Math. Soc. 127 (1999), 3573-3581
MSC (1991): Primary 47H09, 47H10
Published electronically: May 6, 1999
MathSciNet review: 1616654
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Abstract: We prove that any Banach space $X$ whose Banach-Mazur distance to a Hilbert space is less than $\sqrt {\frac{5+\sqrt {13}}{2} }$ has the fixed point property for nonexpansive mappings.


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Additional Information

Pei-Kee Lin
Affiliation: Department of Mathematics, University of Memphis, Memphis, Tennessee 38152
Email: linpk@mathsci.math.memphis.edu

DOI: https://doi.org/10.1090/S0002-9939-99-04971-0
Received by editor(s): January 28, 1997
Received by editor(s) in revised form: February 16, 1998
Published electronically: May 6, 1999
Additional Notes: The work was done while the author was visiting the University of Texas at Austin. The author wishes to thank V. Mascioni, E. Odell and H. Rosenthal for their hospitality, particularly to V. Mascioni and E. Odell for their valuable discussion
Communicated by: Dale E. Alspach
Article copyright: © Copyright 1999 American Mathematical Society