Banach-compact operators, $\mathcal{A}$-precompactness, and frames in Hilbert $C^{\ast }$-modules

Denis Fufaev, Evgenij Troitsky

For a pair of Hilbert $C^{\ast }$-modules $\mathcal{M},\mathcal{N}$ over a $C^{\ast }$-algebra $\mathcal{A}$, there are two notions of ``rank-one operators'': $θ_{x,y} : \mathcal{M} \to \math…