Spectral inclusion for doubly commuting subnormal $n$-tuples
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- by Raul E. Curto PDF
- Proc. Amer. Math. Soc. 83 (1981), 730-734 Request permission
Abstract:
Let $S = ({S_1}, \ldots ,{S_n})$ be a doubly commuting $n$-tuple of subnormal operators on a Hilbert space $\mathcal {H}$ and $N = ({N_1}, \ldots ,{N_n})$ be its minimal normal extension acting on a Hilbert space $\mathcal {K} \supset \mathcal {H}$. We show that $\text {Sp}(S,\mathcal {H}) \supset \text {Sp}(N,\mathcal {K})$ and ${\text {Sp}(S,\mathcal {H}) \subset \text {p}\text {.c}{\text {.h}}\text {.(Sp(}}N,\mathcal {K}))$, where ${\text {Sp}}$ denotes Taylor spectrum and p.c.h. polynomially convex hull.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 730-734
- MSC: Primary 47B20; Secondary 47A10
- DOI: https://doi.org/10.1090/S0002-9939-1981-0630045-6
- MathSciNet review: 630045