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Invertible composition operators on $ L^{2}(\lambda )$


Author: Raj Kishor Singh
Journal: Proc. Amer. Math. Soc. 56 (1976), 127-129
MSC: Primary 47B37
DOI: https://doi.org/10.1090/S0002-9939-1976-0399938-X
MathSciNet review: 0399938
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Abstract: Let $ {C_\phi }$ be a composition operator on $ {L^2}(\lambda )$, where $ \lambda $ is a $ \sigma $-finite measure defined on the Borel subsets of a standard Borel space. In this paper a necessary and sufficient condition for the invertibility of $ {C_\phi }$ is given in terms of invertibility of $ \phi $. Also all invertible composition operators on $ {L^2}({\mathbf{R}})$ induced by monotone continuous functions are characterised.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0399938-X
Keywords: Composition operators, standard Borel space, measurable transformations, Cantor function, monotone continuous function
Article copyright: © Copyright 1976 American Mathematical Society

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