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Hilbert C*-模的内射包络
引用本文:许天周,蔡涛,李炳照. Hilbert C*-模的内射包络[J]. 北京理工大学学报(英文版), 2001, 10(2): 119-124
作者姓名:许天周  蔡涛  李炳照
作者单位:北京理工大学应用数学系,
摘    要:采用同调理论的观点探讨了C 代数上HilbertC 模作为对象和有界模算子作为态射构成的范畴 .研究C 代数上HilbertC 模扩张的内射性和内射包络 ,通过内射性和本性给出内射包络的特征描述 .证明了如果一个C 代数的HilbertC 模的内射包络存在 ,则在H等距意义下是唯一的 .其次给出了HilbertC 模的扩张是内射包络 ,当且仅当此扩张是内射的和本性的 .进一步得到在H等距意义下W 代数上的任何HilbertC 模都有唯一的一个内射包络而且HilbertC 模的内射包络是它的一个极大本性扩张

关 键 词:C代数  HilbertC模  内射包络
收稿时间:2000-10-25

Injective Envelopes of a Hilbert C*Module
XU Tian zhou,CAI Tao and LI Bing zhao. Injective Envelopes of a Hilbert C*Module[J]. Journal of Beijing Institute of Technology, 2001, 10(2): 119-124
Authors:XU Tian zhou  CAI Tao  LI Bing zhao
Affiliation:Dept. of Applied Mathematics, Beijing Institute of Technology, Beijing100081, China;Dept. of Applied Mathematics, Beijing Institute of Technology, Beijing100081, China;Dept. of Applied Mathematics, Beijing Institute of Technology, Beijing100081, China
Abstract:As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelopes of an extension of a Hilbert C * modules over a C * algebra is introduced, and is characterized in terms of the injectivity and essence. It is shown that every Hilbert C * module has a unique (up to H isometrics) injective envelope if it exists. It is also shown that an extension of a Hilbert C * module is an injective envelope if and only if it is an injective and essential extension. Moreover, every Hilbert C * module over a W * algebra has a unique (up to H isometrics) injective envelope and the injective envelope of a Hilbert C * module H is maximal essential extension of H .
Keywords:C * algebra  Hilbert C * module  injective envelope
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