可伴算子保持Hilbert C~*-模中g-框架的充要条件

A Necessary and Sufficient Condition on the Preservation of g-Frames in Hilbert C~*-Modules with Adjointable Operators

利用算子理论方法证明了可伴算子保持Hilbert C~*-模中的g-框架当且仅当它是单射且有闭的值域,这修正了已有的一个结果。

The present paper proves, by utilizing the method of operator theory, that an adjointable operator preserves g-frames in Hilbert C ＊- modules if and only if it is an injective operator with closed range, which provides a correction to one existing corresponding result.