Conditional expectations on Riesz spaces |
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Authors: | Wen-Chi Kuo |
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Affiliation: | School of Mathematics, University of the Witwatersrand, Private Bag 3, PO WITS 2050, South Africa |
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Abstract: | Conditional expectations operators acting on Riesz spaces are shown to commute with a class of principal band projections. Using the above commutation property, conditional expectation operators on Riesz spaces are shown to be averaging operators. Here the theory of f-algebras is used when defining multiplication on the Riesz spaces. This leads to the extension of these conditional expectation operators to their so-called natural domains, i.e., maximal domains for which the operators are both averaging operators and conditional expectations. The natural domain is in many aspects analogous to L1. |
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Keywords: | Averaging operators f-Algebras Conditional expectations Riesz spaces |
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