Conditional expectations and interpolation of linear operators on ordered ideals between $L^1(0,1)$ and $L^\infty(0,1)$

Abstract

The monograph contains the detailed exposition of the results obtained by the author during the last several years. In particular it contains an improvement of the well known Calderon - Ryff interpolation theorem and description of "verifying" operators of conditional mathematical expectations {if such an operator leaves an order ideal in $L^1% invariant, then the ideal is an interpolation space}.