Hilbert C*-模上的酉系统

目的在研究作用在HilbertC*-模上酉系统的框架向量和框架表示的一些性质的基础上,主要给出并证明HilbertC*-模上特殊酉系统的膨胀定理。方法借助几何膨胀原理,用算子代数的方法。结果对作用在HilbertC*-模上酉半群的某完全正规紧框架向量,必能找到一个更大模及其上的酉半群的它的完全游荡向量。结论由于HilbertC*-模不一定有标准正交基,这样通过膨胀,得到更大模上的标准正交基,从而可通过引入框架变换,在这两个模之间建立联系,进而研究HilbertC*-模上框架的可补与不相交性。

Frame vectors for unitary system on Hilbert C * -modules

Aim On the bases of the study on the properties of the frame vectors and representation for unitary system acting on Hilbert C*-modules,the dilation theory of particular unitary system acting on Hilbert C*-modules is obtained and proved.Methods The geometric dilation and operator algebras methods are used.Results For compete the normal tight frame vectors for unitary semi-group acting on Hilbert C*-modules,the competitive wandering vectors must be found.Conclusion Because the orthonormal basis can't be found in Hilbert C*-modules usually,the orthonormal basis can be found in larger module by dilation,then the relation between this two modules can be stated by introducing the frame transform,it is helpful for the study of complementary and disjointness about frame on Hilbert C*-module.