  To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a
locally compact space $\Si$ endowed with a Radon measure, one associates a
coorbit theory converting spaces of functions on $\Si$ in spaces of vectors
comparable with $\H$. If the continuous frame is provided by the action of a
suitable family of bounded operators on a fixed window, a symbolic calculus
emerges, assigning operators in $\H$ to functions on $\Si$. We give some
criteria of relative compactness for sets and for families of compact
operators, involving tightness properties in terms of objects canonically
associated to the frame. Particular attention is dedicated to a magnetic
version of the pseudodifferential calculus.
