Every $L_{p}$ operator is an $L_{2}$ operator
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- by W. B. Johnson and L. Jones PDF
- Proc. Amer. Math. Soc. 72 (1978), 309-312 Request permission
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
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W. B. Johnson, B. Maurey, G. Schechtman and L. Tzafriri, Symmetric structures in Banach spaces, (submitted).
W. B. Johnson and E. W. Odell.
- Bernard Maurey, Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces $L^{p}$, Astérisque, No. 11, Société Mathématique de France, Paris, 1974 (French). With an English summary. MR 0344931
- 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 271721, DOI 10.1007/BF02771562
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 309-312
- MSC: Primary 47B38; Secondary 46E99
- DOI: https://doi.org/10.1090/S0002-9939-1978-0507330-1
- MathSciNet review: 507330