Characterizations of conditional expectation operators for \(L_ p\)- valued functions on a general measure space (Q752441)

For a \(\sigma\)-finite measure space (\(\Omega\),\({\mathcal A},\mu)\) and a Banach space E, the author studies the problem under which conditions a contractive projection on \(L^ 1(\Omega,{\mathcal A},\mu;E)\) can be represented as a conditional expectation operator. An important case of this problem was solved by \textit{D. Landers} and \textit{L. Rogge} [Proc. Am. Math. Soc. 81, 107-110 (1981; Zbl 0471.60013)]; see also the author's earlier work [Osaka J. Math. 23, 313-324 (1986; Zbl 0605.60007)] and [Osaka J. Math. 25, 105-113 (1988; Zbl 0646.60005)]. The present paper is rather technical and contains numerous misprints.