مشخصات پژوهش

This paper considers von Neumann-Schatten p-Bessel sequences, von Neumann-Schatten p-frames and von Neumann-Schatten q-Riesz bases. All sequences, consisting of operators from a separable Banach space X into the von Neumann-Schatten p-class Cp, which are von Neumann-Schatten p- Bessel sequences are characterized and it is shown that the set of all von Neumann-Schatten p-Bessel sequences can be considered as a Banach algebra. Also, some necessary and sufficient conditions for a reflexive Banach space to possess von Neumann-Schatten p-frames or von Neumann-Schatten q-Riesz bases are presented. Moreover, the stability of von Neumann-Schatten p-frames and von Neumann-Schatten q-Riesz bases under different kinds of perturbations is studied, especially some sufficient conditions for the preservation of the frame property under perturbations are derived.