Spectral multiplicity for tensor products of normal operators

Author:
Edward A. Azoff

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

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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 ${N_1} \otimes {N_2}$.

- 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 https://doi.org/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**

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Article copyright:
© Copyright 1981
American Mathematical Society