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浙江大学学报（理学版）
浙江大学学报（理学版）  2019, Vol. 46 Issue (5): 529-536    DOI: 10.3785/j.issn.1008-9497.2019.05.003
数学与计算机科学     
连续广义框架的算子刻画
张伟
河南财经政法大学 数学与信息科学学院，河南 郑州 450046
Operator characterizations of continuous g-frames.
ZHANG Wei
School of Mathematics and Information Sciences, Henan University of Economics and Law, Zhengzhou 450046, China
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摘要： 连续广义预框架算子是算子理论应用于连续广义框架理论的一类重要算子。利用连续广义预框架算子，刻画了连续广义框架、Parseval连续广义框架、连续广义Riesz基及连续广义标准正交基；利用算子工具，构造了新的连续广义框架、Parseval连续广义框架、连续广义Riesz基及连续广义标准正交基,并给出了相应的算子刻画；建立了连续广义预框架算子与强不相交性、不相交性以及强互补对之间的关系；最后，利用已建立的刻画结果，得到了两连续广义框架之和保持框架性质的算子刻画。
关键词： 连续广义框架;  连续广义标准正交基;  不相交性    
Abstract: Continuous g-preframe operator is an important operator for the application of operator theory to the study of the continuous g-frame theory. The characterization of continuous g-frames, Parseval continuous g-frames, continuous g-Riesz bases and continuous g-orthonormal bases can be realized in term of the continuous g-preframe operator; By adopting operator methods, the new continuous g-frames, Parseval continuous g-frames, continuous g-Riesz bases and continuous g-orthonormal bases are constructed and characterized in term of the operators; The link between continuous g-preframe operator and strong disjointness, disjointness, strongly complementary pair is built, respectively; Finally, using the established characterization results, the operator characterization of the sum preserving properties of the two continuous g-frames is obtained.
Key words: continuous g-frames    continuous g-orthonormal bases    disjointness
收稿日期: 2018-06-13 出版日期: 2019-09-25
CLC:  O174.2  
基金资助: 国家自然科学基金资助项目(1127103).
作者简介: 张伟(1979—)，ORCID: http://orcid.org/0000-0002-2533-0204，男，博士，讲师，主要从事小波分析、框架理论及其应用研究， E-mail：zwfylhappy@126.com.
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引用本文:

张伟. 连续广义框架的算子刻画[J]. 浙江大学学报（理学版）, 2019, 46(5): 529-536.

ZHANG Wei. Operator characterizations of continuous g-frames.. Journal of Zhejiang University (Science Edition), 2019, 46(5): 529-536.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2019.05.003    或    https://www.zjujournals.com/sci/CN/Y2019/V46/I5/529

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