Compact and "compact" operators on the standard Hilbert module over a   $W^*$ algebra
  We construct a topology on the standard Hilbert module $l^2(\mathcal A)$ over a unital $W^*$-algebra $\mathcal A$ such that any "compact" operator, (i.e.\ any operator in the norm closure of the linear span of the operators of the form $x\mapsto\left<y,x\right>z$) maps bounded sets into totally bounded sets. 
Dragoljub J Ke\v{c}ki\'c and Zlatko Lazovi\'c
math.OA math.FA