Properties of bounded representations for G-frames

The purpose of the paper is to analyze g-frames of the form {phi T-i is an element of B(H, K)}(i=0)(infinity), where T is an element of B(H) and phi is an element of B(H, K), and discuss the properties of the operator T. We consider stability of g-Riesz sequences of the form {phi T-i is an element of B(H, K)}(i=0)(infinity). Finally, a weighted representation of a g frame is introduced and some of its properties are presented. We provide a sufficient condition for a given g-frame Lambda = {Lambda(i) is an element of B(H, K)}(i=1)(infinity) to be represented by an operator T is an element of B(H) and a sequence {a(i)}(i=1)(infinity).