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Generalized \(a\)-Weyl’s theorem for direct sums. (English) Zbl 1258.47008

Summary: If \(T\) and \(S\) are Hilbert space operators obeying a generalized a-Weyl’s theorem, then it does not necessarily imply that the direct sum \(T\oplus S\) obeys a generalized a-Weyl’s theorem. We explore certain conditions on \(T\) and \(S\) so that the direct sum \(T\oplus S\) obeys a generalized a-Weyl’s theorem.

MSC:

47A11 Local spectral properties of linear operators
47A53 (Semi-) Fredholm operators; index theories
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