Operator Characterizations, Rigidity and Constructions of (Ω, μ)-Frames. (17th February 2018)

• Record Type: Journal Article
• Authors: Guo, Xunxiang
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 3(2018)
• Page Start: 346
• Page End: 360
• Publication Date: 2018-02-17
• Subjects: Analysis operator -- (Ω, μ)-frame -- pair of dual (Ω, μ)-frame -- strongly disjoint -- super (Ω, μ)-frame; 42C15 -- 46B15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1364265
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, first, we give some operator characterizations of (Ω, μ )-frames. We obtain that normalized tight (Ω, μ )-frames are precisely the (Ω, μ )-frames which are unitary equivalent to normalized tight (Ω, μ )-frames for some closed subspace ℳ of L 2 (Ω, μ ) and (Ω, μ )-frames are precisely the (Ω, μ )-frames which are similar to normalized tight (Ω, μ )-frames for some closed subspace ℳ of L 2 (Ω, μ ). We also characterize the alternate dual (Ω, μ )-frames through an operator equation. Then we establish some rigidity in the pairs of dual (super) (Ω, μ )-frames related with disjointness. Finally, we consider the constructions of (Ω, μ )-frames, including the constructions of new (Ω, μ )-frames or new pair of dual (Ω, μ )-frames from known ones and the constructions of the canonical dual of a (Ω, μ )-frame under certain conditions, which generalize the corresponding results on discrete frames.