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A Theorem on Isometries and the Application of it to the Isometries of Hp(S) for 2 < p < ∞

Published online by Cambridge University Press:  20 November 2018

Frank Forelli
Frank Forelli*
Affiliation:
University of Wisconsin, Madison, Wisconsin
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Let X and Y be sets, let λ be a bounded positive measure on X, and let μ be a bounded positive measure on Y. Furthermore let M be a subalgebra of L∞(λ), let p ∈ (0, ∞), and let A be a linear transformation of M into Lp(μ) such that

for all f in M.

In § 2 of this paper we will prove the following theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 2 , April 1973 , pp. 284 - 289
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Forelli, F., The isometries of Hp, Can. J. Math. 16 (1964), 721–728.Google Scholar
2. Schneider, R. B., Isometries of Hp(Un), Can. J. Math. 25 (1973), 92–95.Google Scholar