Group Riesz and Frame Sequences: The Bracket and the Gramian
Abstract
Given a discrete group and a unitary representation on a Hilbert space $\mathcal{H}$, we prove that the notions of operator Bracket map and Gramian coincide on a dense set of $\mathcal{H}$. As a consequence, combining this result with known frame theory, we can recover in a simple way all previous Bracket characterizations of Riesz and frame sequences generated by a single element under a unitary representation.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2016
- DOI:
- 10.48550/arXiv.1608.02767
- arXiv:
- arXiv:1608.02767
- Bibcode:
- 2016arXiv160802767B
- Keywords:
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- Mathematics - Functional Analysis
- E-Print:
- arXiv admin note: text overlap with arXiv:1506.08942