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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Normal and quasinormal composition operators


Author: Robert Whitley
Journal: Proc. Amer. Math. Soc. 70 (1978), 114-118
MSC: Primary 47B38; Secondary 47B15
MathSciNet review: 492057
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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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DOI: https://doi.org/10.1090/S0002-9939-1978-0492057-5
Keywords: Composition operator, normal operator, quasinormal operator
Article copyright: © Copyright 1978 American Mathematical Society