CONSTRUCTIVE COMPACT LINEAR MAPPINGS

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dc.contributor.authorNGWA, Matthias
dc.date.accessioned2014-02-13T10:22:12Z
dc.date.available2014-02-13T10:22:12Z
dc.date.issued1997-07
dc.descriptionA thesis submitted to the Postgraduate School, Ahmadu Bello University, Zaria-Nigeria in partial fulfilment of the requirements for the degree of Master of Science. (JULY, 1997)en_US
dc.description.abstractThis dissertation opens with a discussion of the distinction between the classical and constructive notions of Mathematics. There then follows a description of the three main varieties of modern constructive mathematics: Bishop's constructive mathematics, the recursive constructive mathematics of the Russian School of Markov, and Brouwcr's intuitionistic mathematics. We investigate the relationship between compactness, finite rank and located kernel for a bounded linear mapping of a normed space into a finitedimensional space in a constructive setting. One of the main results is that a bounded linear mapping of a normed space onto a finite-dimensional normed space is constructively compact if and only if its kernel is located. We proceed with the investigation of compact operators on a Hilbert space, and compact linear mappings of a normed space, within the framework of Bishop's constructive mathematics. We characterise the compactness of a bounded linear mapping of a Hilbert space H into C", and prove the theorems: Let A and B be compact operators on a Hilbert space H, let C be an operator on H and let a £ C Then aA is compact, A + B is compact, the Hilbert adjoint A* is compact; An operator on a Hilbert space has an adjoint if and only if it is weakly compact. We also look at constructive substitutes for the classically well-known theorems on compact linear mappings: T is compact if and only if T* is compact; if S is bounded linear operator and if T is compact, then TS is compact; if S and T are compact, then S+T is compact.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/1376
dc.language.isoenen_US
dc.subjectCONSTRUCTIVE,en_US
dc.subjectCOMPACT,en_US
dc.subjectLINEAR,en_US
dc.subjectMAPPINGS.en_US
dc.titleCONSTRUCTIVE COMPACT LINEAR MAPPINGSen_US
dc.typeThesisen_US
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