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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] B. Maurey, Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces $ {L^p}$, Astérisque, No. 11, Soc. Math. de France, Paris, 1974. MR 49 #9670. MR 0344931 (49:9670)
  • [4] H. 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 (42:6602)

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Article copyright: © Copyright 1978 American Mathematical Society

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