The group of automorphisms of $L_{\infty }$ is algebraically reflexive

Félix Cabello Sánchez. "The group of automorphisms of $L_{∞}$ is algebraically reflexive." Studia Mathematica 161.1 (2004): 19-32. <http://eudml.org/doc/285240>.

@article{FélixCabelloSánchez2004,
abstract = {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.},
author = {Félix Cabello Sánchez},
journal = {Studia Mathematica},
keywords = {reflexivity; automorphism group; isometry group; Banach algebras of measurable functions},
language = {eng},
number = {1},
pages = {19-32},
title = {The group of automorphisms of $L_\{∞\}$ is algebraically reflexive},
url = {http://eudml.org/doc/285240},
volume = {161},
year = {2004},
}

TY - JOUR
AU - Félix Cabello Sánchez
TI - The group of automorphisms of $L_{∞}$ is algebraically reflexive
JO - Studia Mathematica
PY - 2004
VL - 161
IS - 1
SP - 19
EP - 32
AB - 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.
LA - eng
KW - reflexivity; automorphism group; isometry group; Banach algebras of measurable functions
UR - http://eudml.org/doc/285240
ER -