Spectral properties of elementary operators. II
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- by Lawrence A. Fialkow PDF
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Abstract:
Let $A = ({A_1}, \ldots ,{A_n})$ and $B = ({B_1}, \ldots ,{B_n})$ denote commutative $n$-tuples of operators on a Hilbert space $\mathcal {H}$. Let ${R_{AB}}$ denote the elementary operator on $\mathcal {L}(\mathcal {H})$ defined by ${R_{AB}}(X) = {A_1}X{B_1} + \cdots + {A_n}X{B_n}$. We obtain new expressions for the essential spectra of ${R_{AB}}$ and ${R_{AB}}|\mathcal {J}$ (the restriction of ${R_{AB}}$ to a norm ideal $\mathcal {J}$ of $\mathcal {L}(\mathcal {H})$). We also study isolated points of joint spectra defined in the sense of ${\text {R}}$. Harte.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 290 (1985), 415-429
- MSC: Primary 47A10; Secondary 47A53
- DOI: https://doi.org/10.1090/S0002-9947-1985-0787973-9
- MathSciNet review: 787973