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博碩士論文 etd-0713109-165356 詳細資訊
Title page for etd-0713109-165356
論文名稱
Title
算子代數上的線性保正交性映射
Linear Orthogonality Preservers of Operator Algebras
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
44
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2009-07-02
繳交日期
Date of Submission
2009-07-13
關鍵字
Keywords
保正交性映射、標準算子代數、算子代數、不相交結構
operator algebras, orthogonality preservers, standard operator algebras, disjointness structures, orthogonality structures
統計
Statistics
本論文已被瀏覽 5781 次,被下載 1343
The thesis/dissertation has been browsed 5781 times, has been downloaded 1343 times.
中文摘要
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。
Abstract
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.
目次 Table of Contents
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
參考文獻 References
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(2003), 231–239.
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[12] H.-L. Gau, J.-S. Jeang and N.-C. Wong, Biseparating linear maps between continuous
vector-valued function spaces, J. Australian Math. Soc., Series A, 74 (2003), no. 1, 101–
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Linear Maps Between C0(­)-Modules, preprint.
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algebras with Hausdorff Spectrum, J. Math. Anal. Appl., to appear.
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