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On the dimension of injective Banach spaces


Author: S. Argyros
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
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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 [Enhancements On Off] (What's this?)

  • [1] S. Argyros, Weak compactness in $ {L^1}(\lambda )$ and injective Banach spaces (to appear).
  • [2] A. Grothendieck, Sur les applications lineaires faiblement compactes d' espaces du type $ C(K)$, Canad. J. Math. 5 (1953), 129-173. MR 0058866 (15:438b)
  • [3] R. Haydon, On dual $ {L^1}$-spaces and injective bidual Banach spaces, Israel J. Math. 31 (1979), 142-152. MR 516250 (80e:46013)
  • [4] H. P. Rosenthal, On injective Banach spaces $ {L^\infty }(\mu )$ for finite measures $ \mu $, Acta Math. 124 (1970), 205-247. MR 0257721 (41:2370)
  • [5] -, On relatively disjoint families of measures with some applications to Banach spaces theory, Studia Math. 37 (1970), 13-36. MR 0270122 (42:5015)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0550510-9
Article copyright: © Copyright 1980 American Mathematical Society

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