Operator Characterizations, Rigidity and Constructions of (Ω, μ)-Frames

被引:3
|
作者
Guo, Xunxiang [1 ]
机构
[1] Southwestern Univ Finance & Econ, Dept Math, Chengdu 611130, Sichuan, Peoples R China
关键词
Analysis operator; (Omega; mu)-frame; pair of dual (Omega; strongly disjoint; super; FRAMES;
D O I
10.1080/01630563.2017.1364265
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, first, we give some operator characterizations of (Omega, mu)-frames. We obtain that normalized tight (Omega, mu)-frames are precisely the (Omega, mu)-frames which are unitary equivalent to normalized tight (Omega, mu)-frames for some closed subspace M of L-2 (Omega, mu) and (Omega, mu)-frames are precisely the (Omega, mu)-frames which are similar to normalized tight (Omega, mu)-frames for some closed subspace M of L-2 (Omega, mu). We also characterize the alternate dual (Omega, mu)-frames through an operator equation. Then we establish some rigidity in the pairs of dual (super) (Omega, mu)-frames related with disjointness. Finally, we consider the constructions of (Omega, mu) frames, including the constructions of new (Omega, mu)-frames or new pair of dual(Omega, mu)-frames from known ones and the constructions of the canonical dual of a (Omega, mu)-frame under certain conditions, which generalize the corresponding results on discrete frames.
引用
收藏
页码:346 / 360
页数:15
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