State diagrams for bounded and unbounded linear operators

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dc.contributor.advisorCross, Ron Wen_ZA
dc.contributor.authorO'Connor, B Jen_ZA
dc.date.accessioned2016-03-28T14:25:40Z
dc.date.available2016-03-28T14:25:40Z
dc.date.issued1990en_ZA
dc.descriptionBibliography: pages 107-110.en_ZA
dc.description.abstractThe theme of this thesis is the construction of state diagrams and their implications. The author generalises most of the theorems in Chapter II of Goldberg [Gl] by dropping the assumption that the doin.ain of the operator is dense in X . The author also presents the standard Taylor-Halberg-Goldberg state diagrams [Gl, 61, 66]. Chapters II and III deal with F₊- and F₋-operators, which are generalisations of the ф₊- and ф₋-operators in Banach spaces of Gokhberg-Krein [GK]. Examples are given of F₊- and F₋-operators. Also, in Chapter III, the main theorems needed to construct the state diagrams of Chapter IV are discussed. The state diagrams of Chapter IV are based on states corresponding to F₊- and F₋-operators; in addition state diagrams relating T and T˝ under the assumptions ϒ(T) > 0 and ϒ(T΄) > 0 are derived. Second adjoints are important in Tauberian Theory (see Cross [Cl]). Chapters I and IV are the main chapters. In Chapter I of this thesis the author modifies many of the proofs appearing in Goldberg [Gl), to take account of the new definition of the adjoint.en_ZA
dc.identifier.apacitationO'Connor, B. J. (1990). <i>State diagrams for bounded and unbounded linear operators</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/18245en_ZA
dc.identifier.chicagocitationO'Connor, B J. <i>"State diagrams for bounded and unbounded linear operators."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1990. http://hdl.handle.net/11427/18245en_ZA
dc.identifier.citationO'Connor, B. 1990. State diagrams for bounded and unbounded linear operators. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - O'Connor, B J AB - The theme of this thesis is the construction of state diagrams and their implications. The author generalises most of the theorems in Chapter II of Goldberg [Gl] by dropping the assumption that the doin.ain of the operator is dense in X . The author also presents the standard Taylor-Halberg-Goldberg state diagrams [Gl, 61, 66]. Chapters II and III deal with F₊- and F₋-operators, which are generalisations of the ф₊- and ф₋-operators in Banach spaces of Gokhberg-Krein [GK]. Examples are given of F₊- and F₋-operators. Also, in Chapter III, the main theorems needed to construct the state diagrams of Chapter IV are discussed. The state diagrams of Chapter IV are based on states corresponding to F₊- and F₋-operators; in addition state diagrams relating T and T˝ under the assumptions ϒ(T) > 0 and ϒ(T΄) > 0 are derived. Second adjoints are important in Tauberian Theory (see Cross [Cl]). Chapters I and IV are the main chapters. In Chapter I of this thesis the author modifies many of the proofs appearing in Goldberg [Gl), to take account of the new definition of the adjoint. DA - 1990 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1990 T1 - State diagrams for bounded and unbounded linear operators TI - State diagrams for bounded and unbounded linear operators UR - http://hdl.handle.net/11427/18245 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/18245
dc.identifier.vancouvercitationO'Connor BJ. State diagrams for bounded and unbounded linear operators. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1990 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/18245en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.subject.otherLinear operatorsen_ZA
dc.titleState diagrams for bounded and unbounded linear operatorsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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