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Polaroid type operators under perturbations

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Aiena P., Aponte E.

Studia Mathematica

2013

tom 214

nr 2

121-136

A bounded operator T defined on a Banach space is said to be polaroid if every isolated point of the spectrum is a pole of the resolvent. The "polaroid" condition is related to the conditions of being left polaroid, right polaroid, or a-polaroid. In this paper we explore all these conditions under commuting perturbations K. As a consequence, we give a general framework from which we obtain, and also extend, recent results concerning Weyl type theorems (generalized or not) for T + K, where K is an algebraic or a quasi-nilpotent operator commuting with T.

Ograniczanie wyników

1 Studia Mathematica

1 Aiena P.

1 Aponte E.

1 2013

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Polaroid type operators under perturbations