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

 

Characterization of $ p$-predictors


Authors: D. Landers and L. Rogge
Journal: Proc. Amer. Math. Soc. 76 (1979), 307-309
MSC: Primary 47H99; Secondary 60A10
MathSciNet review: 537095
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Abstract: Let $ (\Omega ,\mathcal{A},P)$ be a probability space and $ 1 < p < \infty $. It is shown that each operator $ T:{L_p}(\Omega ,\mathcal{A},P) \to {L_p}(\Omega ,\mathcal{A},P)$ which is homogeneous, constant preserving, positive, quasi-additive and fulfills Dykstra's condition is an p-predictor with respect to a suitable $ \sigma $-field, i.e. a nearest point projection onto a closed subspace $ {L_p}(\Omega ,\mathcal{B},P)$, where $ \mathcal{B} \subset \mathcal{A}$ is a $ \sigma $-field. None of the conditions for T can be dispensed without compensation.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0537095-X
PII: S 0002-9939(1979)0537095-X
Keywords: Projection, $ {L_p}$-spaces, conditional expectation
Article copyright: © Copyright 1979 American Mathematical Society