Hilbert C~*-模中g-Riesz基的新刻画

New Characterizations of g-Riesz Bases in Hilbert C~*-Modules

利用算子理论方法证明了Hilbert C~*-模上的可伴算子序列是g-Riesz基且有唯一对偶g-框架当且仅当相应的合成算子是一线性同胚,这修正了已有的一个结论.进一步,作为该结果的直接应用,给出了Hilbert C~*-模中的g-Riesz基具有唯一对偶g-框架的保界等价刻画.

he present paper proves, by utilizing the method of operator theory, that a sequence of adjointable operators on a Hilbert C ＊ -module is a g-Riesz basis with unique dual g-frame if and only if the corresponding synthesis operator is a homeomorphism, which provides a correction to one existing conclusion and further, as a direct application of this result, it gives an equivalent characterization for g-Riesz bases with unique dual g-frames in Hil- bert C＊-modules, which preserves the g-frame hounds.