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.
Aiena, P., Neumann, M.M. (2013). On the stability of the localized single-valued extension property under commuting perturbations. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 141(Volume 141, Issue 6), 2039-2050 [10.1090/S0002-9939-2013-11635-7].
On the stability of the localized single-valued extension property under commuting perturbations
AIENA, Pietro;
2013-01-01
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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