G-FRAMES AND THEIR DUALS FOR HILBERT C∗-MODULES

Abstract

Abstract. Certain facts about frames and generalized frames (g-frames) are extended for the g-frames for Hilbert C∗-modules. It is shown that g-frames for Hilbert C∗-modules share several use-ful properties with those for Hilbert spaces. We also characterize the operators which preserve the class of g-frames for Hilbert C∗-modules. Moreover, a necessary and sufficient condition is obtained for an operator T whose corresponding singleton set {T} is a g-frame. Finally, some characterizations of dual g-frames for Hilbert spaces and Hilbert C∗-modules are given. 1

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oai:CiteSeerX.psu:10.1.1.906.3098Last time updated on 11/1/2017

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