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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0275143-8
PII: S 0002-9939(1971)0275143-8
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