Spectral multiplicity for tensor products of normal operators
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- by Edward A. Azoff
- Proc. Amer. Math. Soc. 81 (1981), 50-54
- DOI: https://doi.org/10.1090/S0002-9939-1981-0589134-7
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Abstract:
Two normal operators ${N_1}$ and ${N_2}$ are constructed such that for any pair ${m_1}$ and ${m_2}$ of their respective multiplicity functions, the ’convolution’ $({m_1} * {m_2})(\lambda ) \equiv \Sigma \{ {m_1}({\lambda _1}) \cdot {m_2}({\lambda _2})|{\lambda _1} \cdot {\lambda _2} = \lambda \}$ fails to be a multiplicity function for the tensor product ${N_1} \otimes {N_2}$.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
- Edward A. Azoff and Kevin F. Clancey, Spectral multiplicity for direct integrals of normal operators, J. Operator Theory 3 (1980), no. 2, 213–235. MR 578941
- K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, No. 3, Academic Press, Inc., New York-London, 1967. MR 0226684
Bibliographic Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 50-54
- MSC: Primary 47B15
- DOI: https://doi.org/10.1090/S0002-9939-1981-0589134-7
- MathSciNet review: 589134