On the Geometric Structure of Minimal Dilations on Hilbert C*-Modules

被引:0
|
作者
Popovici, D. [1 ]
机构
[1] West Univ Timisoara, Dept Math, Timisoara 1900, Romania
来源
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 1998年 / 17卷 / 02期
关键词
Hilbert C*-modules; adjointable contractions; Wold-type decompositions; isometric and unitary dilations;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We build a unitary extension for an isometry on a Hilbert C*-module and then, with this extension help, we obtain the minimal unitary dilation for an adjointable contraction starting from one of its isometric dilations. Having as a starting point a result of B.Sz. - Nagy and C. Foias regarding the geometric structure of the minimal unitary dilations for Hilbert space contractions we prove that this structure maintains itself on Hilbert modules. Finally, we present a necessary and sufficient condition on the minimal isometric dilation in order to admits a Wold-type decomposition, condition which also assures the complementability of the residual part space of the minimal unitary dilation.
引用
收藏
页码:379 / 392
页数:14
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