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Proceedings of the American Mathematical Society

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A uniformly convex Banach space with a Schauder basis which is subsymmetric but not symmetric


Author: Lakhpat R. Pujara
Journal: Proc. Amer. Math. Soc. 54 (1976), 207-210
MSC: Primary 46B15
MathSciNet review: 0402472
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Abstract: An example of a uniformly convex Banach space with a basis $ ({x_i})$ is contructed such that $ ({x_i})$ is subsymmetric but not symmetric.


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

  • [1] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR 0117523
  • [2] T. Figiel and W. B. Johnson, A uniformly convex Banach space which contains no 𝑙_{𝑝}, Compositio Math. 29 (1974), 179–190. MR 0355537
  • [3] D. J. H. Garling, Symmetric bases of locally convex spaces, Studia Math. 30 (1968), 163–181. MR 0230105
  • [4] Ivan Singer, Bases in Banach spaces. I, Springer-Verlag, New York-Berlin, 1970. Die Grundlehren der mathematischen Wissenschaften, Band 154. MR 0298399

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0402472-1
Keywords: Uniformly convex space, subsymmetric basis, symmetric basis
Article copyright: © Copyright 1976 American Mathematical Society