四元数Hilbert空间中近似对偶与对偶标架

Approximately Dual and Dual Frames in Quaternionic Hilbert Spaces

四元数Hilbert空间在应用物理科学特别是量子物理中占有重要地位.本文讨论四元数Hilbert空间的标架理论,引入了四元数Hilbert空间中近似对偶标架的概念,刻画了(近似)对偶标架,给出了由一个(近似)对偶标架对构造其它(近似)对偶标架对的一些充分条件,得到了(近似)对偶标架稳定性的若干结果.

Quaternionic Hilbert spaces play an important role in applied physical sciences especially in quantum physics.This paper addresses the frame theory in quaternionic Hilbert spaces.We introduce the notion of approximately dual frames in quaternionic Hilbert spaces.Then we characterize(approximately) dual frames;present some sufficient conditions for constructing other(approximately) dual frame pairs from one(approximately) dual frame pair;and obtain some stability results on(approximately) dual frames.