Conditional expectations generating the commutants of subalgebras of $L^infty$

Alan Lambert

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J. Korean Math. Soc. 1999; 36(4): 699-705

Printed July 1, 1999

Conditional expectations generating the commutants of subalgebras of $L^infty$

Alan Lambert

Abstract

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Abstract

Given a probability space and a subsigma algebra $\mathcal{A}$, each measure equivalent to the probability measure generates a different conditional expectation operator. We characterize those which act boundedly on the original $L^2$ space, and show there are sufficiently many such conditional expectations to generate the commutant of $L^\infty \left( \mathcal{A}% \right) .$

Keywords: conditional expectation, sigma algebras, commutants

MSC numbers: 47C15, 47B38