6533b873fe1ef96bd12d4b9c

RESEARCH PRODUCT

Property (M) and the weak fixed point property

Brailey SimsJesús García Falset

subject

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsApproximation propertyApplied MathematicsGeneral MathematicsTopological tensor productEberlein–Šmulian theoremBanach spaceUniformly convex spaceFixed-point propertyOpial propertyInterpolation spaceMathematics

description

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.

https://doi.org/10.1090/s0002-9939-97-03953-1