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Continuity of Drazin and generalized Drazin inversion in Banach algebras
(Stellenbosch : Stellenbosch University, 201303)Please refer to full text to view abstract. 
Fredholm theory in general Banach algebras
(Stellenbosch : University of Stellenbosch, 201003)ENGLISH ABSTRACT: This thesis is a study of a generalisation, due to R. Harte (see [9]), of Fredholm theory in the context of bounded linear operators on Banach spaces to a theory in a Banach algebra setting. A bounded ... 
Rank one and finite rank elements of Banach algebras
(Stellenbosch : Stellenbosch University, 200712)ENGLISH ABSTRACT: Let A be a unital complex Banach algebra, which we shall simply refer to as a Banach algebra. An element u in A is single if xuy = 0, where x, y E A, implies that xu = 0 or uy = 0. We say that u acts ... 
Spectrum preserving linear mappings between Banach algebras
(Stellenbosch : Stellenbosch University, 200304)ENGLISH ABSTRACT: Let A and B be unital complex Banach algebras with identities 1 and I' respectively. A linear map T : A + B is invertibility preserving if Tx is invertible in B for every invertible x E A. We say that ...