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.
Reference:
O'Connor, B. 1990. State diagrams for bounded and unbounded linear operators. University of Cape Town.
O'Connor, B. J. (1990). State diagrams for bounded and unbounded linear operators. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/18245
O'Connor, B J. "State diagrams for bounded and unbounded linear operators." Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1990. http://hdl.handle.net/11427/18245
O'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/11427/18245