A decomposition of a measure space with respect to a multiplication operator
Abstract: Let A be a bounded multiplication operator on , where is a complete separable metric space and m a Borel measure. A set of measure zero can be removed from so that the multiplicity function of A is equal to the cardinality of the preimage. In the proof, is decomposed into subsets of simple multiplicity.
-  M. B. Abrahamse and Thomas L. Kriete, The spectral multiplicity of a multiplication operator, Indiana Univ. Math. J. 22 (1972/73), 845–857. MR 0320797, https://doi.org/10.1512/iumj.1973.22.22072
-  H. L. Royden, Real analysis, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. MR 0151555
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Keywords: Multiplication operator, spectral multiplicity
Article copyright: © Copyright 1980 American Mathematical Society