Abstract
In this note, property (ω) and property (ω1)are variants of Weyl’s theorem. By means of topological uniform descent, the sufficient and necessary conditions of a bounded linear operator defined on a Hilbert space that satisfies property (ω1) and property (ω1)is studied. Moreover, property 1 (ω1)and property (ω1)of 2 × 2 operator matrices are discussed as well.
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