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Proceedings of the American Mathematical Society

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

 

 

Convergence sets in reflexive Banach spaces


Author: Bruce Calvert
Journal: Proc. Amer. Math. Soc. 47 (1975), 423-428
DOI: https://doi.org/10.1090/S0002-9939-1975-0355534-0
MathSciNet review: 0355534
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Abstract: A closed linear subspace $ M$ of a reflexive Banach space $ X$ with $ X$ and $ {X^ \ast }$ strictly convex is the range of a linear contractive projection iff $ J(M)$ is a linear subspace of $ {X^ \ast }$. Hence the convergence set of a net of linear contractions is the range of a contractive projection if $ X$ and $ {X^ \ast }$ are locally uniformly convex.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0355534-0
Keywords: Strictly convex, locally uniformly convex, contractive projection, convergence set, mean ergodic theorem
Article copyright: © Copyright 1975 American Mathematical Society