A Kadison Kastler row metric and intermediate subalgebras

Liam Dickson

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arXiv · 1404.3070

A Kadison Kastler row metric and intermediate subalgebras

Liam Dickson

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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.

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Liam Dickson. 2014-08-20. A Kadison Kastler row metric and intermediate subalgebras. https://arxiv.org/abs/1404.3070

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