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A Note on a Class of Operators
Author(s) -
Patel S. M.
Publication year - 1977
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19770780132
Subject(s) - mathematics , class (philosophy) , closure (psychology) , pure mathematics , range (aeronautics) , combinatorics , discrete mathematics , computer science , law , artificial intelligence , materials science , political science , composite material
The aim of this note is to study the spectral properties of the LUECKE's class R of operators T such that ‖( T – zI ) −1 ‖=1/ d ( z, W ( T )) for all z ∉ CLW ( T ), where CLW ( T ) is the closure of the numerical range W ( T ) of T and d ( z, W ( T )) is the distance from z to W ( T ). The main emphasis is on the investigation of those properties of operators of class R which are either similar to or distinct from those of operators satisfying the growth condition ( G 1 ).