G-FRAMES AND THEIR DUALS FOR HILBERT C*-MODULES

Certain facts about frames and generalized frames (g-frames) are extended for the g-frames for Hilbert C*-modules. It is shown that g-frames for Hilbert C*-modules share several useful properties with those for Hilbert spaces. We also characterize the operators which preserve the class of g-frames for Hilbert C*-modules. Moreover, a necessary and sufficient condition is obtained for an operator T whose corresponding singleton set fTg is a g-frame. Finally, some characterizations of dual g-frames for Hilbert spaces and Hilbert C*-modules are given.