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Topological Uniform Descent, Quasi-Fredholmness and Operators Originated from Semi-B-Fredholm Theory

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Abstract

In this paper we study operators originated from semi-B-Fredholm theory and as a consequence we get some results regarding boundaries and connected hulls of the corresponding spectra. In particular, we prove that a bounded linear operator T acting on a Banach space, having topological uniform descent, is a BR operator if and only if 0 is not an accumulation point of the associated spectrum \(\sigma _\mathbf{R}(T)=\{\lambda \in \mathbb {C}:T-\lambda I\notin \mathbf{R}\}\), where \(\mathbf{R}\) denote any of the following classes: upper semi-Weyl operators, Weyl operators, upper semi-Fredholm operators, Fredholm operators, operators with finite (essential) descent and \(\mathbf{BR}\) the B-regularity associated to \(\mathbf{R}\) as in Berkani (Studia Mathematica 140(2):163–174, 2000). Under the stronger hypothesis of quasi-Fredholmness of T,  we obtain a similar characterisation for T being a \(\mathbf{BR}\) operator for much larger families of sets \(\mathbf{R}.\)

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Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000, Niš, Serbia

    Snežana Č. Živković-Zlatanović

  2. Laboratory LAGA, Department of Mathematics, Science Faculty of Oujda, University Mohammed I, Oujda, Morocco

    Mohammed Berkani

Authors
  1. Snežana Č. Živković-Zlatanović
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  2. Mohammed Berkani
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Correspondence to Snežana Č. Živković-Zlatanović.

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Communicated by Jussi Behrndt, Fabrizio Colombo, Sergey Naboko.

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The author is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 174007.

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Živković-Zlatanović, S.Č., Berkani, M. Topological Uniform Descent, Quasi-Fredholmness and Operators Originated from Semi-B-Fredholm Theory. Complex Anal. Oper. Theory 13, 3595–3622 (2019). https://doi.org/10.1007/s11785-019-00920-3

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