Compact and “compact” operators on standard Hilbert modules over $W^{*}$-algebras

We construct a topology on the standard Hilbert module l2(A) over a unital W∗-algebra 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↦z〈y,x〉) maps bounded sets into totally bounded sets.