Noncommutative Shift-Invariant Spaces
Functional Analysis
2015-07-01 v1 Group Theory
Operator Algebras
Abstract
The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A theory of reproducing systems in such modular structures is developed, providing a general framework that includes fundamental results of shift-invariant spaces. In particular, general characterizations of Riesz and frame sequences associated to group representations are provided, extending previous results for abelian groups and for cyclic subspaces of unitary representations of noncommutative discrete groups.
Cite
@article{arxiv.1506.08942,
title = {Noncommutative Shift-Invariant Spaces},
author = {Davide Barbieri and Eugenio Hernández and Victoria Paternostro},
journal= {arXiv preprint arXiv:1506.08942},
year = {2015}
}