Operator Characterizations, Rigidity and Constructions of (Ω, μ)-Frames

In this paper, first, we give some operator characterizations of (Omega, mu)-frames. We obtain that normalized tight (Omega, mu)-frames are precisely the (Omega, mu)-frames which are unitary equivalent to normalized tight (Omega, mu)-frames for some closed subspace M of L-2 (Omega, mu) and (Omega, mu)-frames are precisely the (Omega, mu)-frames which are similar to normalized tight (Omega, mu)-frames for some closed subspace M of L-2 (Omega, mu). We also characterize the alternate dual (Omega, mu)-frames through an operator equation. Then we establish some rigidity in the pairs of dual (super) (Omega, mu)-frames related with disjointness. Finally, we consider the constructions of (Omega, mu) frames, including the constructions of new (Omega, mu)-frames or new pair of dual(Omega, mu)-frames from known ones and the constructions of the canonical dual of a (Omega, mu)-frame under certain conditions, which generalize the corresponding results on discrete frames.