Hostname: page-component-7b7567c8c-lpg2g Total loading time: 0 Render date: 2026-11-15T15:43:41.663Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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.

Information

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

1. Garsia, A., Topics in almost everywhere convergence (Markham, Chicago).Google Scholar
2. Rudin, W., Real and complex analysis (McGraw-Hill, 1974).Google Scholar
3. Stein, E. M., Topics in harmonic analysis (Princeton, 1970).Google Scholar
4. Yosida, K., Functional analysis, 4th Ed. (Springer, 1974).Google Scholar