Spectra of constructs of a system of operators
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- by Angel Carrillo and Carlos Hernández PDF
- Proc. Amer. Math. Soc. 91 (1984), 426-432 Request permission
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.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 426-432
- MSC: Primary 47A60; Secondary 46M05, 47A10
- DOI: https://doi.org/10.1090/S0002-9939-1984-0744643-5
- MathSciNet review: 744643