Weyl Type Theorems for Left and Right Polaroid Operators
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- Aiena, P., Aponte, E. & Balzan, E. Integr. Equ. Oper. Theory (2010) 66: 1. doi:10.1007/s00020-009-1738-2
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A bounded operator defined on a Banach space is said to be polaroid if every isolated point of the spectrum is a pole of the resolvent. In this paper we consider the two related notions of left and right polaroid, and explore them together with the condition of being a-polaroid. Moreover, the equivalences of Weyl type theorems and generalized Weyl type theorems are investigated for left and a-polaroid operators. As a consequence, we obtain a general framework which allows us to derive in a unified way many recent results, concerning Weyl type theorems (generalized or not) for important classes of operators.