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.References
- M. B. Abrahamse and Thomas L. Kriete, The spectral multiplicity of a multiplication operator, Indiana Univ. Math. J. 22 (1972/73), 845–857. MR 320797, DOI 10.1512/iumj.1973.22.22072
- H. L. Royden, Real analysis, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1963. MR 0151555
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