四元数Hilbert空间中近似对偶与对偶标架

张伟, 李云章

数学学报 ›› 2021, Vol. 64 ›› Issue (4) : 613-626.

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数学学报 ›› 2021, Vol. 64 ›› Issue (4) : 613-626. DOI: 10.12386/A2021sxxb0053
论文

四元数Hilbert空间中近似对偶与对偶标架

    张伟1, 李云章2
作者信息 +

Approximately Dual and Dual Frames in Quaternionic Hilbert Spaces

    Wei ZHANG1, Yun Zhang LI2
Author information +
文章历史 +

摘要

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.

Abstract

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.

关键词

四元数Hilbert空间 / 对偶标架 / 近似对偶标架

Key words

quaternionic Hilbert space / dual frame / approximately dual frame

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张伟, 李云章. 四元数Hilbert空间中近似对偶与对偶标架. 数学学报, 2021, 64(4): 613-626 https://doi.org/10.12386/A2021sxxb0053
Wei ZHANG, Yun Zhang LI. Approximately Dual and Dual Frames in Quaternionic Hilbert Spaces. Acta Mathematica Sinica, Chinese Series, 2021, 64(4): 613-626 https://doi.org/10.12386/A2021sxxb0053

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基金

国家自然科学基金资助项目（11971043）；河南省高等学校重点科研项目（20A110013）
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