## State diagrams for bounded and unbounded linear operators

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.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.identifier.apacitation | O'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/11427/18245 | en_ZA |

dc.identifier.chicagocitation | O'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/11427/18245 | 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.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.uri | http://hdl.handle.net/11427/18245 | |

dc.identifier.vancouvercitation | 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 | en_ZA |

dc.language.iso | eng | en_ZA |

dc.publisher.department | Department of Mathematics and Applied Mathematics | en_ZA |

dc.publisher.faculty | Faculty of Science | en_ZA |

dc.publisher.institution | University of Cape Town | |

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 | Master Thesis | |

dc.type.qualificationlevel | Masters | |

dc.type.qualificationname | MSc | en_ZA |

uct.type.filetype | Text | |

uct.type.filetype | Image | |

uct.type.publication | Research | en_ZA |

uct.type.resource | Thesis | en_ZA |

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