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Spectral inclusion for subnormal $ n$-tuples

Author: Mihai Putinar
Journal: Proc. Amer. Math. Soc. 90 (1984), 405-406
MSC: Primary 47B20; Secondary 47A10
MathSciNet review: 728357
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Abstract: Let $ S$ be a subnormal operator on a Hilbert space and let $ N$ be its minimal extension. Then a celebrated theorem due to P. Halmos asserts that $ {\text{Sp}}(N) \subset {\text{Sp}}(S)$, denoting by $ {{\text{S}}_{\text{P}}}$ the spectrum. This note contains a multidimensional version, with respect to Taylor's joint spectrum, of this spectral inclusion theorem.

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

  • [1] R. E. Curto, Spectral inclusion for doubly commuting subnormal $ n$-tuples, Proc. Amer. Math. Soc. 83 (1981), 730-734. MR 630045 (82j:47030)
  • [2] P. Halmos, A Hilbert space problem book, Van Nostrand, Princeton, N. J., 1967. MR 0208368 (34:8178)

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Keywords: Subnormal operator, commuting $ n$-tuple, Taylor's joint spectrum, minimal normal extension
Article copyright: © Copyright 1984 American Mathematical Society

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