Abstract
In this paper we study the relationships between the B-Browder spectra and some other spectra originating from Fredholm theory and B-Fredholm theory. This study is done by using the localized single valued extension property. In particular, we shall see that many spectra coincide in the case that a bounded operator T, or its dual T*, or both, admits the single valued extension property.
Similar content being viewed by others
References
Aiena, P.: Fredholm and Local Spectral Theory, with Application to Multipliers, Kluwer Acad. Publishers, 2004
Aiena, P.: Classes of Operators Satisfying a-Weyl’s theorem, Studia Math., 169 (2005), 105–122
Aiena, P.: Quasi Fredholm operators and localized SVEP, Acta Sci. Mat. (Szeged), 73 (2007), 251–263
Aiena, P., Biondi M.T., Carpintero C.: On Drazin invertibility, Proc. Amer. Math. Soc., 136, (2008), 2839–2848
Aiena, P., Carpintero C.: Single valued extension property and semi-Browder spectra, Acta Sci. Math. (Szeged), 20 (2003), 1027–1040
Aiena, P., Miller, T.L.: On generalized a-Browder’s theorem, Studia Math., 180(3) (2007), 285–300
Aiena, P., Rosas, E.: The single valued extension property at the points of the approximate point spectrum, J. Math. Anal. Appl., 279(1), (2003), 180–188
Aiena, P., Sanabria, J.E.: On left and right poles of the resolvent, to appear in Acta Sci. Math. (Szeged),(2008)
Berkani, M.: On a class of quasi-Fredholm operators, Int. Equa. Oper. Theory, 34 (1999), 244–249
Berkani, M.: Restriction of an operator to the range of its powers, Studia Math., 140 (2000), 163–175
Berkani, M., Sarih, M.: On semi B-Fredholm operators, Glasgow Math. J., 43 (2001), 457–465
Finch, J.K.: The single valued extension property on a Banach space, Pacific J. Math., 58 (1975), 61–69
Heuser, H.: Functional Analysis, Marcel Dekker, New York, 1982
Laursen, K.B., Neumann, M.M.: Introduction to local spectral theory, Clarendon Press, Oxford, 2000
Mbekhta, M., Müller, V.: On the axiomatic theory of the spectrum II, Studia Math., 119 (1996), 129–147
Miller, T.L., Miller, V.G., Smith, R.C.: Bishop’s property (β) and Cesáro operator, J. London Math. Soc., 58 (1998), 197–207
Rakočevič, V.: Semi-Browder operators and perturbations, Studia Math., 122 (1996), 131–137
Rakočevič, V.: Semi-Fredholm operators with finite ascent or descent and perturbations, Proc. Amer. Math. Soc., 123 (1995), 3823–3825
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Carpintero, C.R., García, O., Rosas, E.R. et al. B-Browder spectra and localized SVEP. Rend. Circ. Mat. Palermo 57, 239–254 (2008). https://doi.org/10.1007/s12215-008-0017-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12215-008-0017-4