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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Characterization of $p$-predictors
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by D. Landers and L. Rogge PDF
Proc. Amer. Math. Soc. 76 (1979), 307-309 Request permission

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.
References
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 76 (1979), 307-309
  • MSC: Primary 47H99; Secondary 60A10
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0537095-X
  • MathSciNet review: 537095