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

Abstract

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 thatfor all f in M.In § 2 of this paper we will prove the following theorem.