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Proceedings of the American Mathematical Society

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



Every $ L\sb{p}$ operator is an $ L\sb{2}$ operator

Authors: W. B. Johnson and L. Jones
Journal: Proc. Amer. Math. Soc. 72 (1978), 309-312
MSC: Primary 47B38; Secondary 46E99
MathSciNet review: 507330
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Abstract: If T is a bounded linear operator on $ {L_p}(\mu ),1 \leqslant p < \infty ,\mu $ a probability measure, then, after an appropriate change of density, T acts as a bounded operator on $ {L_2}$.

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

  • [1] W. B. Johnson, B. Maurey, G. Schechtman and L. Tzafriri, Symmetric structures in Banach spaces, (submitted).
  • [2] W. B. Johnson and E. W. Odell.
  • [3] Bernard Maurey, Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces 𝐿^{𝑝}, Société Mathématique de France, Paris, 1974 (French). With an English summary; Astérisque, No. 11. MR 0344931
  • [4] Haskell P. Rosenthal, On the subspaces of 𝐿^{𝑝} (𝑝>2) spanned by sequences of independent random variables, Israel J. Math. 8 (1970), 273–303. MR 0271721

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Article copyright: © Copyright 1978 American Mathematical Society