The alternative Daugavet property of C *-algebras and JB *-triples

✍ Scribed by Miguel Martín

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 168 KB
• Volume: 281
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200510608

✦ Synopsis

Abstract

A Banach space X is said to have the alternative Daugavet property if for every (bounded and linear) rank‐one operator T: X → X there exists a modulus one scalar ω such that ∥Id+ωT ∥ = 1 + ∥T ∥. We give geometric characterizations of this property in the setting of C *‐algebras, JB *‐triples, and of their isometric preduals. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)