Holomorphic automorphisms and collective compactness in J*-algebras of operator

✍ Scribed by José M. Isidro

• Book ID: 111488397
• Publisher: SP Versita
• Year: 2007
• Tongue: English
• Weight: 207 KB
• Volume: 5
• Category: Article
• ISSN: 1895-1074
• DOI: 10.2478/s11533-007-0016-2

✦ Synopsis

Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball B A in a J * -algebra A of operators. Let F be the family of all collectively compact subsets W contained in B A . We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family F is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when A is a Cartan factor.