Spectral inclusion for subnormal $n$-tuples
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- by Mihai Putinar PDF
- Proc. Amer. Math. Soc. 90 (1984), 405-406 Request permission
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
- Raul E. Curto, Spectral inclusion for doubly commuting subnormal $n$-tuples, Proc. Amer. Math. Soc. 83 (1981), no. 4, 730–734. MR 630045, DOI 10.1090/S0002-9939-1981-0630045-6
- Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 405-406
- MSC: Primary 47B20; Secondary 47A10
- DOI: https://doi.org/10.1090/S0002-9939-1984-0728357-3
- MathSciNet review: 728357