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Keywords
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Banach space, K-frame, von Neumann–Schatten p-frame, von Neumann–Schatten K*-atomic system,
von Neumann–Schatten K-p-frame
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Abstract
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We introduce von Neumann–Schatten K-p-frames and von Neumann–Schatten K*-atomic systems, where
K is a bounded operator on a separable Banach space, and we collect some relationships between these
two concepts. Also, we characterize von Neumann–Schatten K-p-frames in terms of a range inclusion
property and show that they are stable under different kinds of perturbations and the action of some
bounded operators. Moreover, we introduce and characterize the notions of K-duals and K*-duals
and obtain some of their properties.
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