Banach Journal of Mathematical Analysis

Wandering subspaces and fusion frame generators for unitary systems

Aifang Liu and Pengtong Li

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Abstract

This work is inspired by the study of wandering vectors and frame vectors for unitary systems. We investigate the structure and properties of complete wandering subspaces for unitary systems, and, in particular, we consider the unitary systems with a structure similar to wavelet systems. Given a unitary system with a complete wandering subspace, a necessary and sufficient condition for a closed subspace to be a Parseval fusion frame generator is obtained. Moreover, we study the dilation property for Parseval fusion frame generators for unitary groups.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 4 (2016), 848-863.

Dates
Received: 20 October 2015
Accepted: 31 January 2016
First available in Project Euclid: 7 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1475870135

Digital Object Identifier
doi:10.1215/17358787-3649722

Mathematical Reviews number (MathSciNet)
MR3555753

Zentralblatt MATH identifier
1354.42052

Subjects
Primary: 42C15: General harmonic expansions, frames
Secondary: 42C40: Wavelets and other special systems 47D03: Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}

Keywords
unitary system local commutant wandering subspace fusion frame generator dilation

Citation

Liu, Aifang; Li, Pengtong. Wandering subspaces and fusion frame generators for unitary systems. Banach J. Math. Anal. 10 (2016), no. 4, 848--863. doi:10.1215/17358787-3649722. https://projecteuclid.org/euclid.bjma/1475870135


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