Stability of the fixed point property of Hilbert spaces
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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.References
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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
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3573-3581
- MSC (1991): Primary 47H09, 47H10
- DOI: https://doi.org/10.1090/S0002-9939-99-04971-0
- MathSciNet review: 1616654