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

Socpus ID

84899897015 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84899897015

This document is currently not available here.

Share

COinS