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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$l^{\infty }/c_{0}$ has no equivalent strictly convex norm
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by J. Bourgain PDF
Proc. Amer. Math. Soc. 78 (1980), 225-226 Request permission

Abstract:

It is shown that the quotient space ${l^\infty }/{c_0}$ does not admit an equivalent strictly convex norm.
References
  • Mahlon M. Day, Normed linear spaces, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 21, Springer-Verlag, New York-Heidelberg, 1973. MR 0344849
  • Joseph Diestel, Geometry of Banach spaces—selected topics, Lecture Notes in Mathematics, Vol. 485, Springer-Verlag, Berlin-New York, 1975. MR 0461094, DOI 10.1007/BFb0082079
    • —, Private communication.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 78 (1980), 225-226
  • MSC: Primary 46B25; Secondary 46A45
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0550499-2
  • MathSciNet review: 550499