Some Construction of Generalized Frames with Adjointable Operators in Hilbert C∗−modules

Abstract

Generalized frame called g-frame was first proposed using a sequence of adjointable operators to deal with all the existing frames as a united object. In fact, the g-frame is an extension of ordinary frames. Generalized frames with adjointable operators called K-g-frame is a generalization of a g-frame. It can be used to reconstruct elements from the range of a adjointable operator K. K-g-frames have a certain advantage compared with g-frames in practical applications. This paper is devoted to study some properties of K-g-frame in Hilbert C^∗ -module, we characterize the concept of K-g-frame by quotient maps. Also discus some result of the dual K-g-Bessel sequences of K-g-frame in Hilbert C^∗ -module. Our results are more general than those previously obtained. It is shown that the results we obtained can immediately lead to the existing corresponding results in Hilbert Spaces.