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On Drazin Spectral Equation for the Operator Products

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Let X be a Banach space and A ,  B ,  C ,  D be bounded linear operators on X . In this paper we show that the Drazin (resp.… Click to show full abstract

Let X be a Banach space and A ,  B ,  C ,  D be bounded linear operators on X . In this paper we show that the Drazin (resp. generalized Drazin) spectrum of AC coincides with the Drazin (resp. generalized Drazin) spectrum of BD under certain assumptions. Moreover, several interesting Banach space properties, such as SVEP and polaroidness, are considered.

Keywords: drazin spectral; operator products; equation operator; operator; spectral equation

Journal Title: Complex Analysis and Operator Theory
Year Published: 2020

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