Multipliers of generalized frames in Hilbert spaces (Q648467)

The author investigates generalized (\(g\)-) Bessel sequences and generalized (\(g\)-) frames, and introduces the concept of \(g\)-Bessel multipliers. In particular, it is shown that if the symbol \(m\) of a \(g\)-Bessel multiplier belongs to the sequence space \(c_0\), then the operator is compact, and when \(m\in \ell^1, \ell^2\) or \(\ell^p\), then the operator is a trace class, Hilbert-Schmidt or Schatten \(p\)-class operator, respectively. In addition, it is proved that equivalent \(g\)-frames have equivalent multipliers and conversely. Finally, the above concepts are applied to fusion frames (or frames of subspaces).