Hilbert K-模上框架的不相交性及不变量问题

The disjointness and invariant problems of frames on Hilbert K-modules

考虑了紧算子代数模(Hilbert K-模)上的框架。运用泛函分析和算子代数的理论知识,给出并证明了HilbertK-模上框架(强)不相交的充要条件。最后,联系C*-子代数的指标理论,得到了Hilbert C*-子代数中关于不变量问题的两个重要结论。

The frames of modules on compact operator algebras which are called K-modules are considered.The theories of function analysis and operator algebras are used and the equivalent conditions of disjointness of frames on Hilbert K-module are given and proved.Finally,Two important conclusions about invariant problems on Hilbert C＊-subalgebras are obtained by the index theories of C＊-subalgebras When Hilbert C＊-subalgebras are considered as a Hilbert K-module on itself.