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Weyl's theorem for operator matrices

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Abstract

“Weyl's theorem holds” for an operator when the complement in the spectrum of the “Weyl” spectrum” coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. By comparison “Browder's theorem holds” for an operator when the complement in the spectrum of the Weyl spectrum coincides with Riesz points. Weyl's theorem and Browder's theorem are liable to fail for 2×2 operator matrices. In this paper we explore how Weyl's theorem and Browder's theorem survive for 2×2 operator matrices on the Hilbert space.

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Supported in part by BSRI-97-1420 and KOSEF 94-0701-02-01-3.

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Lee, W.Y. Weyl's theorem for operator matrices. Integr equ oper theory 32, 319–331 (1998). https://doi.org/10.1007/BF01203773

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  • DOI: https://doi.org/10.1007/BF01203773

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