A HILBERT C*-MODULE VIEW OF SOME SPACES RELATED TO PROBABILISTIC CONDITIONAL EXPECTATION

Abstract

Measure theoretic conditional expectation is used to construct certain operator spaces. The conditional expectation induces a Hilbert module structure on these spaces. Application is made of Kasparov's theorem to examine certain multiplier and compact operator algebras associated with the module structure. This examination is related to the now classic results on characterizations of conditional expectation type operators.