GENERALIZED FRAMES WITH C*-VALUED BOUNDS AND THEIR OPERATOR DUALS

Abstract

‎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.