  This note is a survey and collection of results, as well as presenting some
original research. For Bessel sequences and frames, the analysis, synthesis and
frame operators as well as the Gram matrix are well-known, bounded operators.
We investigate these operators for arbitrary sequences, which in general lead
to possibly unbounded operators. We characterize various classes of sequences
in terms of these operators and vice-versa. Finally, we classify these
sequences by operators applied on orthonormal bases.
