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Spectra of constructs of a system of operators

Authors: Angel Carrillo and Carlos Hernández
Journal: Proc. Amer. Math. Soc. 91 (1984), 426-432
MSC: Primary 47A60; Secondary 46M05, 47A10
MathSciNet review: 744643
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Abstract: This paper describes the spectrum and the upper and lower Fredholm spectra of $ (n + m)$-tuples $ (F({A_1}), \cdots ,F({A_n}),G({B_1}), \cdots ,G({B_m}))$ of operators, where $ ({A_i})$ and $ ({B_j})$ are systems of operators in two Hilbert spaces $ {\mathcal{H}_1}$ and $ {\mathcal{H}_2}$, and $ F$ and $ G$ are certain linear operators defined on $ \mathcal{L}({\mathcal{H}_i})$. Using spectral mapping theorems the spectra of operators constructed by the action of a polynomial on a system $ (F({A_1}), \cdots ,F({A_n}),G({B_1}), \cdots ,G({B_m}))$ is obtained. In particular, the spectra of the elementary operator and tensor products of operators is determined.

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Keywords: Spectrum, joint spectrum, upper and lower Fredholm spectra, essential spectrum, Fredholm operator, spectral mapping theorem, elementary operator, tensor products
Article copyright: © Copyright 1984 American Mathematical Society

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