Banach-compact operators between Hilbert C*-modules are characterized as those whose image of the unit ball is A-precompact, with ties to frames.
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Banach-compact operators, $\mathcal A$-precompactness, and frames in Hilbert $C^*$-modules
Banach-compact operators between Hilbert C*-modules are characterized as those whose image of the unit ball is A-precompact, with ties to frames.