On Convergence of Conditional Expectation Operators

1994/12/05 by C. Bryan Dawson, Dawson, C. Bryan
Mathematics · #46B #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.math/9412211

openalex publication_date 1994/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given an operator T:U_X(Σ)→ Y or T:U(Σ)→ Y, one may consider the net of conditional expectation operators (T_π) directed by refinement of the partitions π. It has been shown previously that (T_π) does not always converge to T. This paper gives several conditions under which this convergence does occur, including complete characterizations when X=\bold R or when X\sp * has the Radon-Nikodým property.

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