Hilbert C*—模中g—Riesz基的新刻画

2018-05-08 11:11相中启
关键词:算子对偶小波

摘 要 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,給出了Hilbert C*-模中的g-Riesz基具有唯一对偶g-框架的保界等价刻画.

关键词 Hilbert C*-模;g-框架;g-Riesz基;对偶g-框架

中图分类号 O177.1文献标识码 A文章编号 1000-2537(2017)06-0080-07

Abstract The 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 Hilbert C*-modules, which preserves the g-frame bounds.

Key words Hilbert C*-module; g-frame; g-Riesz basis; dual g-frame

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