Browder and Weyl spectra of upper triangular operator matrices | Zendy

B. P. Duggal | Zendy

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Browder and Weyl spectra of upper triangular operator matrices

Author(s) -

B. P. Duggal

Publication year - 2010

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1002111d

Subject(s) - mathematics , banach space , extension (predicate logic) , operator (biology) , mathematics subject classification , type (biology) , pure mathematics , algebra over a field , ecology , biochemistry , chemistry , repressor , biology , computer science , transcription factor , gene , programming language

Let MC = µ A C 0 B ¶ 2 B(X ' X) be an upper triangulat Banach space operator. The relationship between the spectra of MC and M0, and their various distinguished parts, has been studied by a large number of authors in the recent past. This paper brings forth the important role played by SVEP, the single{valued extension property, in the study of some of these relations. Operators MC and M0 satisfying Browder’s, or a-Browder’s, theorem are characterized, and we prove necessary and su‐cient conditions for implications of the type \M0 satisfles a-Browder’s (or a-Weyl’s) theorem () MC satisfles a-Browder’s (resp., a-Weyl’s) theorem" to hold.

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