Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A fixed point property of $ l\sb 1$-product spaces


Authors: Tadeusz Kuczumow, Simeon Reich and Malgorzata Schmidt
Journal: Proc. Amer. Math. Soc. 119 (1993), 457-463
MSC: Primary 47H10; Secondary 46B20
DOI: https://doi.org/10.1090/S0002-9939-1993-1155601-9
MathSciNet review: 1155601
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {X_1}$ and $ {X_2}$ be Banach spaces, and let $ {X_1} \times {X_2}$ be equipped with the $ {l_1}$-norm. If the first space $ {X_1}$ is uniformly convex in every direction, then $ {X_1} \times {X_2}$ has the fixed point property for nonexpansive mappings (FPP) if and only if $ \mathbb{R} \times {X_2}$ (with the $ {l_1}$-norm) does. If $ {X_1}$ is merely strictly convex, $ (\mathbb{R} \times {X_2})$ has the FPP, and $ {C_i} \subset {X_i}$ are weakly compact and convex with the FPP (for $ i = 1,2$), then the fixed point set of every nonexpansive mapping $ T:{C_1} \times {C_2} \to {C_1} \times {C_2}$ is a nonexpansive retract of $ {C_1} \times {C_2}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H10, 46B20

Retrieve articles in all journals with MSC: 47H10, 46B20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1155601-9
Keywords: Nonexpansive mappings, nonexpansive retracts, fixed points, the semi-Opial property
Article copyright: © Copyright 1993 American Mathematical Society