Convergence sets in reflexive Banach spaces
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- by Bruce Calvert PDF
- Proc. Amer. Math. Soc. 47 (1975), 423-428 Request permission
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.References
- S. J. Bernau, Theorems of Korovkin type for $L_{p}$-spaces, Pacific J. Math. 53 (1974), 11–19. MR 393979
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 423-428
- DOI: https://doi.org/10.1090/S0002-9939-1975-0355534-0
- MathSciNet review: 0355534