The group of automorphisms of $L_{∞}$ is algebraically reflexive

• Autorzy: Félix Cabello Sánchez
• Języki publikacji: EN

Abstrakty

EN

We study the reflexivity of the automorphism (and the isometry) group of the Banach algebras $L_{∞}(μ)$ for various measures μ. We prove that if μ is a non-atomic σ-finite measure, then the automorphism group (or the isometry group) of $L_{∞}(μ)$ is [algebraically] reflexive if and only if $L_{∞}(μ)$ is *-isomorphic to $L_{∞}[0,1]$. For purely atomic measures, we show that the group of automorphisms (or isometries) of $ℓ_{∞}(Γ)$ is reflexive if and only if Γ has non-measurable cardinal. So, for most "practical" purposes, the automorphism group of $ℓ_{∞}(Γ)$ is reflexive.

Kategorie tematyczne

• 46L40: Automorphisms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 161
• Numer: 1
• Strony: 19-32

Daty

wydano

2004

Twórcy

autor

Félix Cabello Sánchez

• Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071 Badajoz, Spain

Identyfikatory

DOI

10.4064/sm161-1-2