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Spectrum preserving linear mappings between Banach algebras
(Stellenbosch : Stellenbosch University, 2003-04)
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 ...
Fredholm theory in general Banach algebras
(Stellenbosch : University of Stellenbosch, 2010-03)
ENGLISH ABSTRACT: This thesis is a study of a generalisation, due to R. Harte (see ), of Fredholm theory in the context of bounded linear operators on Banach spaces to a theory in a Banach algebra setting. A bounded ...
Spectral theory in commutatively ordered banach algebras
(Stellenbosch : Stellenbosch University, 2012-12)
ENGLISH ABSTRACT: See full text.
Rank one and finite rank elements of Banach algebras
(Stellenbosch : Stellenbosch University, 2007-12)
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 ...
Continuity of Drazin and generalized Drazin inversion in Banach algebras
(Stellenbosch : Stellenbosch University, 2013-03)
Please refer to full text to view abstract.