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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Pietro Aiena and Michael M. Neumann
Journal: Proc. Amer. Math. Soc. 141 (2013), 2039-2050
MSC (2010): Primary 47A10, 47A11; Secondary 47A53, 47A55
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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Pietro Aiena
Affiliation: Dipartimento di Metodi e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy
Email: paiena@unipa.it

Michael M. Neumann
Affiliation: Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762
Email: neumann@math.msstate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11635-7
PII: S 0002-9939(2013)11635-7
Keywords: Localized single-valued extension property, quasi-nilpotent part, analytic core, Kato decomposition and quasi-Fredholm operators, semi-Browder operators and Riesz operators
Received by editor(s): April 22, 2011
Received by editor(s) in revised form: September 26, 2011
Published electronically: January 7, 2013
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2013 American Mathematical Society