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Characterization of conditional expectations for $M$-space-valued functions

1993

Introduction Let (Ω, Jl, μ) be a probability space, E a Banach space. We consider constant-preserving contractive projections of L^Ω, <Jl, μ, E) into itself. If E=R or E is a strictly-convex Banach space, then it is known (Ando [2], Douglas [3] and Landers and Rogge [6] ) that such operators coincide precisely with the conditional expectation operators. If E=L 1 (X, 5, λ, R), where (X, S, λ) is a localizable measure space, then the author [8] proved that such operators which are translation

doi:10.18910/9980
fatcat:swvxecdsbbd43f55igzpiytvba