G-frames and their duals for Hilbert C*-modules

Abstract

Abstract. Certain facts about frames and generalized frames (g- <br />frames) are extended for the g-frames for Hilbert C*-modules. It is <br />shown that g-frames for Hilbert C*-modules share several useful <br />properties with those for Hilbert spaces. The paper also character- <br />izes the operators which preserve the class of g-frames for Hilbert <br />C*-modules. Moreover, a necessary and suffcient condition is ob- <br />tained for an operator T whose corresponding singleton set {T} to <br />be a g-frame. Finally, some characterizations of dual g-frames for <br />Hilbert spaces and Hilbert C*-modules are given.