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UNBOUNDED B-FREDHOLM OPERATORS ON HILBERT SPACES

2008
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Proceedings of the Edinburgh Mathematical Society
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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

doi:10.1017/s0013091505001574
fatcat:hd43sbluyvcp7oo65qorhk5cm4