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Several Remarks Concerning the Local Theory of L p Spaces

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1850)

Abstract

For the symmetric Xp,wn subspaces of L p , p > 2, we determine the dimension of their approximately Euclidean subspaces and estimate the smallest dimensions of their containing spaces. We also show that a diagonal of the canonical basis of , p > 2, with an unconditional basic sequence in L p whose span is complemented, spans a space which is isomorphic to a complemented subspace of L p .

Mathematics Subject Classification (2000):

  • 46-06
  • 46B07
  • 52-06 60-06

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Correspondence to W. B. Johnson .

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© 2004 Springer-Verlag Berlin/Heidelberg

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Johnson, W.B., Schechtman, G. (2004). Several Remarks Concerning the Local Theory of L p Spaces. In: Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44489-3_13

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  • DOI: https://doi.org/10.1007/978-3-540-44489-3_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22360-3

  • Online ISBN: 978-3-540-44489-3

  • eBook Packages: Springer Book Archive