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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Spectral inclusion for doubly commuting subnormal $ n$-tuples


Author: Raul E. Curto
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
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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}$. We show that Sp$ (S,\mathcal{H}) \supset$   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.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0630045-6
Keywords: Subnormal $ n$-tuple, doubly commuting, spectral inclusion
Article copyright: © Copyright 1981 American Mathematical Society