Abstract

The Banach-Stone problem for Lp-spaces is to assert when a linear isometry between Lp-spaces is a weighted composition operator. We shall show that every σ-finite measure space with Sikorski’s property solves the Banach-Stone probelm. In addition, we show that if X is a totally ordered and Dedekind complete, then every σ-finite μ-separable measure space (X, B, μ) has Sikorski’s property.

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