As a generalization of the traditional frame in Hilbert space,g-frame has many good properties.The stability of g-frame under the action of preframe operator and composition operator is studied by means of op-erator theory,and then the properties of tight g-frame on orthogonal complement are investigated,the necessary and sufficient condition of g-Bessel sequences forming g-Orthonormal basis in Hilbert space H is proved by Schmidt orthogonalization,and the existence of G-biorthogonal sequences for g-Orthonormal basis perturbed by a single-shot operator.
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