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Hilbert空间上的K-框架与K-对偶 被引量：4

K-FRAMES AND K-DUALS IN HILBER SPACES
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摘要 Hilbert空间的K-框架是框架的一种推广,并且与经典框架有许多差别.本文讨论了K-框架与算子K的值域的关系,利用K-框架的合成算子和算子K对K-框架的最优界进行了刻画.此外,我们引入K-对偶的概念,给出了K-对偶的若干性质,并研究了Parseval K-框架的K-对偶的唯一性. K-frames in Hilbert spaces are the generalizations of frames and there are many differences between K-frames and ordinary frames. In this paper, we discuss the relation between a K-frame and the operator K, and characterize the optimal bounds of a K-frame by using the synthesis operator and the operator K. We introduce the definition of K-dual of a K-frame and obtain some properties of K-duals. Also, the uniqueness of the K-dual for a Parseval K-frame is investigated.
作者 李亮 李鹏同
机构地区 南京航空航天大学数学系
出处 《南京大学学报（数学半年刊）》 CAS 2015年第1期74-88,共15页 Journal of Nanjing University(Mathematical Biquarterly)
基金 国家自然科学基金(1171151) 江苏省科学基金(BK2011720)资助课题
关键词 框架 K-框架 合成算子 框架界 K-对偶 frame, K-frame, synthesis operator, frame bound, K-dual
分类号 O177.1 [理学—基础数学]
  • 相关文献

参考文献16

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二级参考文献12

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  • 10Gavruta L., New results on frames for operators, Proc. Intern. Conf. Sciences, 11-12 Nov. 2011, Oradea, Accepted.

共引文献10

同被引文献20

引证文献4

二级引证文献3

南京大学学报（数学半年刊）
2015年 第1期

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