State diagrams for bounded and unbounded linear operators

 

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dc.contributor.advisor Cross, Ron W en_ZA
dc.contributor.author O'Connor, B J en_ZA
dc.date.accessioned 2016-03-28T14:25:40Z
dc.date.available 2016-03-28T14:25:40Z
dc.date.issued 1990 en_ZA
dc.identifier.citation O'Connor, B. 1990. State diagrams for bounded and unbounded linear operators. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/18245
dc.description Bibliography: pages 107-110. en_ZA
dc.description.abstract 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. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematics en_ZA
dc.subject.other Linear operators en_ZA
dc.title State diagrams for bounded and unbounded linear operators en_ZA
dc.type Thesis / Dissertation en_ZA
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Masters en_ZA
dc.type.qualificationname MSc en_ZA
uct.type.filetype Text
uct.type.filetype Image


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