Subnormal composition operators

Lambert, Alan

doi:10.1090/S0002-9939-1988-0947651-8

Subnormal composition operators
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Proc. Amer. Math. Soc. 103 (1988), 750-754 Request permission

Abstract:

Let $C$ be the composition operator on ${L^2}(X,\Sigma ,m)$ given by $Cf = f \circ T$, where $T$ is a $\Sigma$-measurable transformation from $X$ onto $X$ and ${T^{ - 1}}/dm$ is strictly positive and bounded. It is shown that $C$ is a subnormal operator if and only if the sequence $dm \circ {T^{ - n}}/dm$ is a moment sequence for almost every point in $X$. Several examples of subnormal composition operators are included.

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The Laplace transform