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Proceedings of the American Mathematical Society

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Conditional expectations and an isomorphic characterization of $ L\sb{1}$-spaces

Author: L. Tzafriri
Journal: Proc. Amer. Math. Soc. 27 (1971), 317-324
MSC: Primary 46.35; Secondary 28.00
MathSciNet review: 0275143
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Abstract: Conditional expectations can be defined in Banach spaces whose elements can be represented as measurable functions. In the present paper it is shown that such a space (precisely a cyclic space) is isomorphic to an $ {L_1}$-space if and only if the conditional expectations act as bounded operators for sufficiently many representations.

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Keywords: Conditional expectation, Banach function spaces, cyclic spaces, $ {L_1}$-spaces, Boolean algebras of projections, isomorphism between Banach spaces
Article copyright: © Copyright 1971 American Mathematical Society

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