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An Extrapolation Theorem for Positive Operators

Published online by Cambridge University Press:  20 November 2018

H. D. B. Miller
H. D. B. Miller*
Affiliation:
University of Toronto, Toronto, Ontario
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Denote by S and M respectively the complex vector spaces of simple and measurable complex valued functions defined on the finite measure space X. Let T be a positive linear map from S to M such that for each p, 1 < p < ∞, sup {||T f||p: f ∈ S, ||f||P ≦ 1} is finit. finite. T then has an extension to a bounded transformation of every LP(X), 1 < p < ∞ , and these extensions are "consistent". The norm of T as a transformation of Lp is denoted ||T||P. The aim of this note is to prove the following theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 2 , 01 April 1978 , pp. 225 - 230
Copyright
Copyright © Canadian Mathematical Society 1978

References

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