Operator space characterizations of C*-algebras and ternary rings

2002/01/21 by Matthew Neal, Bernard Russo
Mathematics · #math.OA #math.FA #msc:46L07 #msc:46L70 #msc:17C65

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published as Pacific Journal of Mathematics 209 No. 2 (2003) 339-364 · 20 pages, latex, submitted in November 2001

arxiv created 2002/01/21 · arxiv updated 2009/11/30

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.

Related

• Geometric characterizations of some classes of operators in C*-algebras and von Neumann algebras
• Metric characterizations of isometries and of unital operator spaces and systems
• Isomorphisms of operator algebras
• Anti-C*-algebras
• The Lattice of C*-covers of an operator algebra