LINEAR ORTHOGONALITY PRESERVERS OF HILBERT C*-MODULES
Publication in refereed journal

香港中文大學研究人員

引用次數
替代計量分析
.

其它資訊
摘要We show in this paper that the module structure and the orthogonality structure of a Hilbert C*-module determine its inner product structure. Let A be a C*-algebra, and E and F be Hilbert A-modules. Assume Phi : E -> F is an A-module map satisfying (A) = 0 whenever < x,y >(A) = 0. Then Phi is automatically bounded. In case Phi is bijective, E is isomorphic to F. More precisely, let J(E) be the closed two-sided ideal of A generated by the set {< x,y >(A) : x,y is an element of E}. We show that there exists a unique central positive multiplier u is an element of M(J(E)) such that (A) = u < x,y >(A) (x,y is an element of E). As a consequence, the induced map Phi(0) : E -> (Phi) over bar((E) over bar) is adjointable, and (Eu-1/2) over bar is isomorphic to (Phi) over bar((E) over bar) as Hilbert A-modules.
著者Leung CW, Ng CK, Wong NC
期刊名稱JOURNAL OF OPERATOR THEORY
詳細描述To ORKTS: This paper accepted for publication in the Journal of Operator Theory
出版年份2014
月份3
日期1
卷號71
期次2
出版社THETA FOUNDATION
頁次571 - 584
國際標準期刊號0379-4024
語言英式英語
關鍵詞auto continuity; Hilbert C*-modules; Orthogonality preservers; Uhl horn theorem
Web of Science 學科類別Mathematics; MATHEMATICS

上次更新時間 2021-25-02 於 01:36