On the dimension of injective Banach spaces
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- by S. Argyros
- Proc. Amer. Math. Soc. 78 (1980), 267-268
- DOI: https://doi.org/10.1090/S0002-9939-1980-0550510-9
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Abstract:
The purpose of this note is to give an affirmative answer, assuming the generalized continuum hypothesis, to a problem of H. Rosenthal on the cardinality of the dimension on injective Banach spaces.References
- S. Argyros, Weak compactness in ${L^1}(\lambda )$ and injective Banach spaces (to appear).
- A. Grothendieck, Sur les applications linéaires faiblement compactes d’espaces du type $C(K)$, Canad. J. Math. 5 (1953), 129–173 (French). MR 58866, DOI 10.4153/cjm-1953-017-4
- Richard Haydon, On dual $L^{1}$-spaces and injective bidual Banach spaces, Israel J. Math. 31 (1978), no. 2, 142–152. MR 516250, DOI 10.1007/BF02760545
- Haskell P. Rosenthal, On injective Banach spaces and the spaces $L^{\infty }(\mu )$ for finite measure $\mu$, Acta Math. 124 (1970), 205–248. MR 257721, DOI 10.1007/BF02394572
- Haskell P. Rosenthal, On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37 (1970), 13–36. MR 270122, DOI 10.4064/sm-37-1-13-36
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 267-268
- MSC: Primary 46B99; Secondary 04A30
- DOI: https://doi.org/10.1090/S0002-9939-1980-0550510-9
- MathSciNet review: 550510