On the stability of the localized single-valued extension property under commuting perturbations

Aiena, Pietro; Neumann, Michael

doi:10.1090/S0002-9939-2013-11635-7

On the stability of the localized single-valued extension property under commuting perturbations
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by Pietro Aiena and Michael M. Neumann

Proc. Amer. Math. Soc. 141 (2013), 2039-2050

DOI: https://doi.org/10.1090/S0002-9939-2013-11635-7

Published electronically: January 7, 2013

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Abstract:

This article concerns the permanence of the single-valued extension property at a point under suitable perturbations. While this property is, in general, not preserved under sums and products of commuting operators, we obtain positive results in the case of commuting perturbations that are quasi-nilpotent, algebraic, or Riesz operators.

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