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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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A decomposition of a measure space with respect to a multiplication operator
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by James S. Howland PDF
Proc. Amer. Math. Soc. 78 (1980), 231-234 Request permission

Abstract:

Let A be a bounded multiplication operator on ${L_2}(\Omega ,m)$, where $\Omega$ is a complete separable metric space and m a Borel measure. A set of measure zero can be removed from $\Omega$ so that the multiplicity function of A is equal to the cardinality of the preimage. In the proof, $\Omega$ is decomposed into subsets of simple multiplicity.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 78 (1980), 231-234
  • MSC: Primary 47B15
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0550502-X
  • MathSciNet review: 550502