Title
Dilations For Systems Of Imprimitivity Acting On Banach Spaces
Keywords
Banach space; Dilation; Frame; Operator-valued measure; Projective isometric representation; System of imprimitivity
Abstract
Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued system of imprimitivity has a dilation to a probability spectral system of imprimitivity acting on a Banach space. This completely generalizes a well-known result which states that every frame representation of a countable group on a Hilbert space is unitarily equivalent to a subrepresentation of the left regular representation of the group. We also prove that isometric group representation induced framings on a Banach space can be dilated to unconditional bases with the same structure for a larger Banach space. This extends several known results on the dilations of frames induced by unitary group representations on Hilbert spaces. © 2014 Elsevier Inc.
Publication Date
6-15-2014
Publication Title
Journal of Functional Analysis
Volume
266
Issue
12
Number of Pages
6914-6937
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1016/j.jfa.2014.02.040
Copyright Status
Unknown
Socpus ID
84899897015 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84899897015
STARS Citation
Han, Deguang; Larson, David R.; Liu, Bei; and Liu, Rui, "Dilations For Systems Of Imprimitivity Acting On Banach Spaces" (2014). Scopus Export 2010-2014. 8453.
https://stars.library.ucf.edu/scopus2010/8453