A new variation of Weyl type theorems and perturbations | Zendy

Junli Shen | Zendy; Alatancang Chen | Zendy

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A new variation of Weyl type theorems and perturbations

Author(s) -

Junli Shen,

Alatancang Chen

Publication year - 2014

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/fil1409899s

Subject(s) - mathematics , nilpotent , property (philosophy) , algebraic number , pure mathematics , rank (graph theory) , type (biology) , connection (principal bundle) , algebra over a field , discrete mathematics , mathematical analysis , combinatorics , geometry , ecology , philosophy , epistemology , biology

In this paper we introduce the new property (aR), which extends property (R) introduced by Aiena and his collaborators. We investigate the property (aR) in connection with Weyl type theorem, and establish sufficient and necessary conditions for which property (aR) holds. We also study the stability of property (aR) under perturbations by finite rank operators, by nilpotent operators, by quasi-nilpotent operators and by algebraic operators commuting with T.

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