Abstract
ABSTRACT The purpose of this paper is to study g-frames having a representation by iterated action of a fixed operator on a single element. It is shown that only some special g-frames have a operator representation. We characterize the g-frames that have such a representation for a bounded operator T, and study the properties of this operator. We also give a characterization of the case where such a representation is possible with a bounded operator T, and calculate the operator T from a g-frame and its dual g-frames. Then we characterize all the dual g-frames that are representable in terms of iterations of a bounded operator. Finally, we discuss the perturbation of operator representations of g-frames under which the perturbation conditions preserve the property of being representable by an operator.
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