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A decomposition of a measure space with respect to a multiplication operator


Author: James S. Howland
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
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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 [Enhancements On Off] (What's this?)

  • [1] M. B. Abrahamse and T. L. Kriete, The spectral multiplicity of a multiplication operator, Indiana J. Math. 22 (1973), 845-857. MR 0320797 (47:9331)
  • [2] H. L. Royden, Real analysis, 2nd ed., Macmillan, New York, 1968. MR 0151555 (27:1540)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0550502-X
Keywords: Multiplication operator, spectral multiplicity
Article copyright: © Copyright 1980 American Mathematical Society

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