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

Denis Fufaev, Evgenij Troitsky

For a couple $\mathcal{M}$, $\mathcal{N}$ of Hilbert $C^{\ast }$-modules over a $C^{\ast }$-algebra $\mathcal{A}$, one has two notions of ``$\mathcal{A}$-rank 1 operators'': $θ_{x,y}:\mathcal M\t…