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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Invertible composition operators on $L^{2}(\lambda )$
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by Raj Kishor Singh PDF
Proc. Amer. Math. Soc. 56 (1976), 127-129 Request permission

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
  • © Copyright 1976 American Mathematical Society
  • 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