Approximately Dual and Dual Frames in Quaternionic Hilbert Spaces
Wei ZHANG1, Yun Zhang LI2
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1. School of Mathematics and Information Sciences, He'nan University of Economics and Law, Zhengzhou 450046, P. R. China; 2. College of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, P. R. China
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.
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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