Regresar

Property (gR) under nilpotent commuting perturbation

Abstract:

The property (gR), introduced in [Aiena, P., Guillen, J. and Peña, P., Property (gR) and perturbations, to appear in Acta Sci. Math. (Szeged), 2012], is an extension to the context of B-Fredholm theory, of property (R), introduced in [Aiena, P., Guillen, J. and Peña, P., Property (R) for bounded linear operators, Mediterr. J. Math. 8 (4), 491-508, 2011]. In this paper we continue the study of property (gR) and we consider its preservation under perturbations by finite rank and nilpotent operators. We also prove that if T is left polaroid (resp. right polaroid) and N is a nilpotent operator which commutes with T then T + N is also left polaroid (resp. right polaroid).