Normal and quasinormal composition operators

Whitley, Robert

doi:10.1090/S0002-9939-1978-0492057-5

Normal and quasinormal composition operators
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by Robert Whitley PDF

Proc. Amer. Math. Soc. 70 (1978), 114-118 Request permission

Abstract:

A bounded linear operator ${C_T}$ on ${L^2}(X,\Sigma ,m)$ is a composition operator if it is induced by a point mapping $T:X \to X$ via ${C_T}f = f \circ T$. Normal and quasinormal composition operators on a finite measure space are characterized: ${C_T}$ is normal iff T is measure preserving and ${T^{ - 1}}(\Sigma )$ is (essentially) all of $\Sigma ;{C_T}$ is quasinormal iff T is measure preserving.

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