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Variations on a-Browder-type theorems. (English) Zbl 06315237
Summary: We introduce and we study the new spectral properties \((SBw)\), \((SBaw)\), \((SBab)\) and \((SBb)\). Among other results, we show that if \(T\) is a bounded linear operator acting on a Banach space \(X\), then \(T\) possesses property \((SBb)\) if and only if \(T\) possesses property \((b)\) and \(\prod^0 (T) = \prod_a (T)\).

MSC:
47A53 (Semi-) Fredholm operators; index theories
47A10 Spectrum, resolvent
47A11 Local spectral properties of linear operators
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