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Property (M) and the weak fixed point property


Authors: Jesús Garcia Falset and Brailey Sims
Journal: Proc. Amer. Math. Soc. 125 (1997), 2891-2896
MSC (1991): Primary 47H09, 47H10, 46B20
DOI: https://doi.org/10.1090/S0002-9939-97-03953-1
MathSciNet review: 1403125
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Abstract: It is shown that in Banach spaces with the property (M) of Kalton, nonexpansive self mappings of nonempty weakly compact convex sets necessarily have fixed points. The stability of this conclusion under renormings is examined and conditions for such spaces to have weak normal structure are considered.


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Additional Information

Jesús Garcia Falset
Affiliation: Departament d’Anàlisi Matematica, Facultat de Matematiques, Universitat de València, Doctor Moliner 50, 46100 Burjassot, Spain
Email: Jesus.Garcia@uv.es

Brailey Sims
Affiliation: Department of Mathematics, The University of Newcastle, New South Wales 2308, Australia
Email: bsims@frey.newcastle.edu.au

DOI: https://doi.org/10.1090/S0002-9939-97-03953-1
Received by editor(s): January 3, 1996
Received by editor(s) in revised form: April 19, 1996
Additional Notes: Partially supported by grant DGICYT PB-1177-c02-02 and a travel grant from the University of Newcastle.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society