Abstract
Property(ω)is a variant of Weyl's theorem.By the property of consistence in Fredholm index,the judgement of property(ω)is studied.Using the relation between a new spectrum defined in view of the property of consistence in Fredholm index and the topological uniform descent,the necessary and sufficient condition for an operator and its conjugate to satisfy property(ω)are given.In addition,the property(ω)of operator matrices is studied.
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