A Kadison Kastler row metric and intermediate subalgebras

In this paper, we introduce a row version of Kadison and Kastler's metric on the set of C*-subalgebras of B(H). By showing C*-algebras have row length (in the sense of Pisier) of at most 2 we show that the row metric is equivalent to the original Kadison–Kastler metric. Ino and Watatani have recently proved that in certain circumstances sufficiently close intermediate C*-algebras occur as small unitary perturbations. By adjusting their arguments to work with the row metric we are able to obtain universal constants independent of inclusions