Weyl's theorem for operator matrices | Zendy

Woo Young Lee | Zendy

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Weyl's theorem for operator matrices

Author(s) -

Woo Young Lee

Publication year - 1998

Publication title -

integral equations and operator theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.121

H-Index - 48

eISSN - 1420-8989

pISSN - 0378-620X

DOI - 10.1007/bf01203773

Subject(s) - mathematics , operator (biology) , pure mathematics , algebra over a field , shift operator , combinatorics , discrete mathematics , compact operator , extension (predicate logic) , biochemistry , chemistry , repressor , computer science , transcription factor , gene , programming language

“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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