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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



$ P$-convexity and $ B$-convexity in Banach spaces

Author: Dean R. Brown
Journal: Trans. Amer. Math. Soc. 187 (1974), 77-81
MSC: Primary 46B10
MathSciNet review: 0333678
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Abstract: Two properties of B-convexity are shown to hold for P-convexity:

(1) Under certain conditions, the direct sum of two P-convex spaces is P-convex.

(2) A Banach space is P-convex if each subspace having a Schauder decomposition into finite dimensional subspaces is P-convex.

References [Enhancements On Off] (What's this?)

  • [1] D. R. Brown, B-convexity and reflexivity in Banach spaces, Trans. Amer. Math. Soc. 187 (1974), 69-76. MR 0333677 (48:12002)
  • [2] D. P. Giesy, On a convexity condition in normed linear spaces, Trans. Amer. Math. Soc. 125 (1966), 114-146. MR 34 #4866. MR 0205031 (34:4866)
  • [3] M. Grinbylum, On the representation of a space of type B in the form of a direct sum of subspaces, Dokl. Akad. Nauk SSSR (N. S.) 70 (1950), 749-752. (Russian) MR 11, 525. MR 0033977 (11:525c)
  • [4] C. A. Kottman, Packing and reflexivity in Banach space, Trans. Amer. Math. Soc. 150 (1970), 565-576. MR 42 #827. MR 0265918 (42:827)
  • [5] A. Pełczyński, A note on the paper of I. Singer, 'Basic sequences and reflexivity of Banach spaces,' Studia Math. 21 (1961/62), 371-374. MR 26 #4156. MR 0146636 (26:4156)
  • [6] F. Ramsey, On a problem of formal logic, Proc. London Math. Soc., (2) 30 (1930), 264-286.

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Keywords: B-convexity, P-convexity, reflexivity, uniform convexity, geometry of the unit ball, Ramsey's theorem, Schauder basis, Schauder decomposition
Article copyright: © Copyright 1974 American Mathematical Society

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