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 $x\mapsto\left z$) maps bounded sets into totally bounded sets.
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