## Subnormal composition operators

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- by Alan Lambert
- Proc. Amer. Math. Soc.
**103**(1988), 750-754 - DOI: https://doi.org/10.1090/S0002-9939-1988-0947651-8
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## 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.## References

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## Bibliographic Information

- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**103**(1988), 750-754 - MSC: Primary 47B20; Secondary 47B38
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947651-8
- MathSciNet review: 947651