Generalized Frames With $C^*$-Valued Bounds and Their Operator Duals

A. Alijani

Certain facts about frames and generalized frames are extended for the new $g$-frames, referred as $*$-$g$-frames, in a Hilbert $C^*$-modules. As a matter of fact, some relations are establish between $*$-frames and $*$-$g$-frames in a Hilbert $C^*$-module. Furthermore, the paper studies the operators associated to a given $*$-$g$-frame, the construction of new $*$-$g$-frames. Moreover, the operator duals for a $*$-$g$-frame are introduced and their properties are investigated. Finally, operator duals of a $*$-$g$-frame are characterized.