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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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 ${N_1} \otimes {N_2}$.


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Article copyright: © Copyright 1981 American Mathematical Society