Group Riesz and Frame Sequences: The Bracket and the Gramian
  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. 
Davide Barbieri, Eugenio Hernandez, Victoria Paternostro
math.FA