dc.contributor.advisor | Doran, Robert S. | |

dc.contributor.author | Fields, Jerry Wayne | en_US |

dc.date.accessioned | 2019-10-11T15:11:02Z | |

dc.date.available | 2019-10-11T15:11:02Z | |

dc.date.created | 1972 | en_US |

dc.date.issued | 1972 | en_US |

dc.identifier | aleph-254627 | en_US |

dc.identifier.uri | https://repository.tcu.edu/handle/116099117/33819 | |

dc.description.abstract | In this dissertation, an effort is made to give sufficient conditions that self-adjoint linear mappings of C*-algebras be C*-homomorphisms. Sufficient conditions are given so that a positive linear functional on a Banach *-algebra is multiplicative. Positive linear mappings of C*-algebras are characterized in terms of the numerical range. If A is a C* -algebra and x in A, the set V(x) = {f(x): f is a pure state on A} is studied. Also, a detailed examination is made of algebras of continuous functions vanishing at infinity on a locally compact Hausdorff space and having values in an arbitrary Banach algebra. These algebras are denoted by C_0 (X, A). If A is a commutative Banach algebra with an approximate identity, then the Shilov boundary of C_0 (X, A) is computed. If A is a C*-algebra, the pure states on C_0 (X, A) are characterized in terms of the pure states on A. If X is compact, it is shown that the pure states on C(X,A) with the weak*- topology is homeomorphic with a topological product. | |

dc.format.extent | iv, 95 leaves, bound | en_US |

dc.format.medium | Format: Print | en_US |

dc.language.iso | eng | en_US |

dc.relation.ispartof | Texas Christian University dissertation | en_US |

dc.relation.ispartof | AS38.F54 | en_US |

dc.subject.lcsh | Banach algebras | en_US |

dc.title | Linear mappings of Banach algebras and Banach algebras of vector-valued functions | en_US |

dc.type | Text | en_US |

etd.degree.department | Department of Mathematics | |

etd.degree.level | Doctoral | |

local.college | College of Science and Engineering | |

local.department | Mathematics | |

local.academicunit | Department of Mathematics | |

dc.type.genre | Dissertation | |

local.subjectarea | Mathematics | |

dc.identifier.callnumber | Main Stacks: AS38 .F54 (Regular Loan) | |

dc.identifier.callnumber | Special Collections: AS38 .F54 (Non-Circulating) | |

etd.degree.name | Doctor of Philosophy | |

etd.degree.grantor | Texas Christian University | |