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Proceedings of the American Mathematical Society

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Spectral multiplicity for tensor products of normal operators

Author: Edward A. Azoff
Journal: Proc. Amer. Math. Soc. 81 (1981), 50-54
MSC: Primary 47B15
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})\vert{\lambda _1} \cdot {\lambda _2} = \lambda \} $ fails to be a multiplicity function for the tensor product $ {N_1} \otimes {N_2}$.

References [Enhancements On Off] (What's this?)

  • [1] M. B. Abrahamse and T. L. Kriete, The spectral multiplicity of a multiplication operator, Indiana Univ. Math. J. 22 (1973), 845-857. MR 0320797 (47:9331)
  • [2] E. Azoff and K. Clancey, Spectral multiplicity for direct integrals of normal operators, J. Operator Theory 3 (1980), 213-235. MR 578941 (83j:47025)
  • [3] K. R. Parthasarathy, Probability measures on metric spaces, Academic Press, New York, 1967. MR 0226684 (37:2271)

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