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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0728357-3
PII: S 0002-9939(1984)0728357-3
Keywords: Subnormal operator, commuting $ n$-tuple, Taylor's joint spectrum, minimal normal extension
Article copyright: © Copyright 1984 American Mathematical Society