We construct a topology on the standard Hilbert module over a unital -algebra such that any “compact” operator (i.e., any operator in the norm closure of the linear span of the operators of the form ) maps bounded sets into totally bounded sets.
"Compact and “compact” operators on standard Hilbert modules over -algebras." Ann. Funct. Anal. 9 (2) 258 - 270, May 2018. https://doi.org/10.1215/20088752-2017-0053