A Kadison Kastler row metric and intermediate subalgebras

Abstract

In this paper we introduce a row version of Kadison and Kastler's metric on the set of C*-subalgebras of $\mathbb{B}(\mathcal{H})$. 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.

Minor changes. To appear in Internat. J. Math

References in corpus (2)

• Decomposable approximations of nuclear C*-algebras
• A remark on the similarity and perturbation problems