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

• Autorzy: José Isidro
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

J*-algebras; Cartan factors; holomorphic automorphisms; Banach-Lie groups; collective compactness

Kategorie tematyczne

• 17B65: Infinite-dimensional Lie (super)algebras
• 17C65: Jordan structures on Banach spaces and algebras
• 22E65: Infinite-dimensional Lie groups and their Lie algebras: general properties
• 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 3
• Strony: 512-522

Daty

wydano

2007-09-01

online

2007-09-01

Twórcy

autor

José Isidro

• Facultad de Matemáticas, Santiago de Compostela

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-007-0016-2