UNBOUNDED B-FREDHOLM OPERATORS ON HILBERT SPACES

M. Berkani, N. Castro-González
2008 Proceedings of the Edinburgh Mathematical Society  
This paper is concerned with the study of a class of closed linear operators densely defined on a Hilbert space H and called B-Fredholm operators. We characterize a B-Fredholm operator as the direct sum of a Fredholm closed operator and a bounded nilpotent operator. The notion of an index of a B-Fredholm operator is introduced and a characterization of B-Fredholm operators with index 0 is given in terms of the sum of a Drazin closed operator and a finite-rank operator. We analyse the properties
more » ... lyse the properties of the powers T m of a closed B-Fredholm operator and we establish a spectral mapping theorem.
doi:10.1017/s0013091505001574 fatcat:hd43sbluyvcp7oo65qorhk5cm4