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Spectral properties of elementary operators. II


Author: Lawrence A. Fialkow
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
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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}}\vert\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.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0787973-9
Article copyright: © Copyright 1985 American Mathematical Society

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