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

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 σ R ( T ) = { λ ∈ C : T - λ I ∉ R } , where 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 BR the B-regularity associated to 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 BR operator for much larger families of sets R .