A note on the characterization of conditional expectation operators

Daniel Eliot Wulbert

Vol. 34 (1970), No. 1, 285–288

DOI: 10.2140/pjm.1970.34.285

Abstract

Let (X,∑ ,μ) be an arbitrary measure space. A complete characterization is presented for the norm one positive projections P of L¹(X,∑ ,μ) into itself such that ∥f∥∞≧∥Pf∥_∞ for each essentially bounded, summable function f.

Mathematical Subject Classification

Primary: 46.35

Secondary: 60.00

Milestones

Received: 18 February 1969

Published: 1 July 1970