Operator space characterizations of C*-algebras and ternary rings

Matthew Neal and Bernard Russo

Vol. 209 (2003), No. 2, 339–364

DOI: 10.2140/pjm.2003.209.339

Abstract

We prove that an operator space is completely isometric to a ternary ring of operators if and only if the open unit balls of all of its matrix spaces are bounded symmetric domains. From this we obtain an operator space characterization of C*-algebras.

Milestones

Received: 22 November 2001

Revised: 25 April 2002

Published: 1 April 2003