臺灣博碩士論文加值系統

Banach-Stone定理（Kadison定理）說兩個交換（一般）C*-代數在 C*-代數（JB*-代數）意義下是同構的若且唯若它們 Banach 空間意義下是同構的。在此，我們感興趣的是利用不同的結構來決定一個 C*-代數。我們想要研究 C*-代數的不相交結構並考察這個結構是否可用來決定一個 C*-代數。
我們至少可以定義四種不同的不相交結構：零乘積、值域正交性、定義域正交性和雙重正交性。在本篇論文中，我們會先研究標準算子代數上的不相交結構。然後將這些結果推廣到有連續跡的 C*-代數上。

The Banach-Stone Theorem (respectly, Kadison Theorem) says that two abelian (respectively, general) C*-algebras are isomorphic as C*-algebras (respectively, JB*-algebras) if and only if they are isomorphic as Banach spaces. We are interested in using different structures to determine C*-algebras. Here, we would like to study the disjointness structures of C*-algebras and investigate if it suffices to determine C*-algebras.
There are at least four versions of disjointness structures: zero product, range orthogonality, domain orthogonality and doubly orthogonality. In this thesis, we first study these disjointness structures in the case of standard operator algebras. Then we extend these results to general C*-algebras, namely, C*-algebras with continuous trace.

Chapter 1: Introduction 1
Chapter 2: Notations and Preliminaries 3
2.1 Disjointness structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Continuous fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 CCR C*-algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 3: Separating linear maps of continuous fields of Banach spaces 12
3.1 Separating maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Biseparating maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Chapter 4: Linear orthogonality preservers of standard operator algebras
19
4.1 Zero product preservers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Range and domain orthogonality preservers . . . . . . . . . . . . . . . . . . 21
4.3 Range-domain and domain-range orthogonality preservers . . . . . . . . . . 23
4.4 Doubly orthogonality preservers . . . . . . . . . . . . . . . . . . . . . . . . 25
Chapter 5: Linear orthogonality preservers of C*-algebras with continuous
traces 27
5.1 Zero product preservers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.2 Singly-orthogonality preservers . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.3 Unsolved problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

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