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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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