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