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Keywords
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Banach space, von Neumann-Schatten p-Bessel sequence, von Neumann-Schatten p-frame, von Neumann-Schatten q-Riesz basis, perturbation.
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Abstract
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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.
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