Locally convex algebras which determine a locally compact group

Gholam Hossein Esslamzadeh, Hossein Javanshiri, and Rasoul Nasr-Isfahani. "Locally convex algebras which determine a locally compact group." Studia Mathematica 233.3 (2016): 197-207. <http://eudml.org/doc/286150>.

@article{GholamHosseinEsslamzadeh2016,
abstract = {There are several algebras associated with a locally compact group 𝓖 which determine 𝓖 in the category of topological groups, such as L¹(𝓖), M(𝓖), and their second duals. In this article we add a fairly large family of locally convex algebras to this list. More precisely, we show that for two infinite locally compact groups 𝓖₁ and 𝓖₂, there are infinitely many locally convex topologies τ₁ and τ₂ on the measure algebras M(𝓖₁) and M(𝓖₂), respectively, such that (M(𝓖₁),τ₁)** is isometrically isomorphic to (M(𝓖₂),τ₂)** if and only if 𝓖₁ and 𝓖₂ are topologically isomorphic. In particular, this leads to a new proof of Ghahramani-Lau's isometrical isomorphism theorem for compact groups, different from those of Ghahramani and J. P. McClure (2006) and Dales et al. (2012).},
author = {Gholam Hossein Esslamzadeh, Hossein Javanshiri, Rasoul Nasr-Isfahani},
journal = {Studia Mathematica},
keywords = {locally compact groups; measure algebra; generalized functions vanishing at infinity; second dual},
language = {eng},
number = {3},
pages = {197-207},
title = {Locally convex algebras which determine a locally compact group},
url = {http://eudml.org/doc/286150},
volume = {233},
year = {2016},
}

TY - JOUR
AU - Gholam Hossein Esslamzadeh
AU - Hossein Javanshiri
AU - Rasoul Nasr-Isfahani
TI - Locally convex algebras which determine a locally compact group
JO - Studia Mathematica
PY - 2016
VL - 233
IS - 3
SP - 197
EP - 207
AB - There are several algebras associated with a locally compact group 𝓖 which determine 𝓖 in the category of topological groups, such as L¹(𝓖), M(𝓖), and their second duals. In this article we add a fairly large family of locally convex algebras to this list. More precisely, we show that for two infinite locally compact groups 𝓖₁ and 𝓖₂, there are infinitely many locally convex topologies τ₁ and τ₂ on the measure algebras M(𝓖₁) and M(𝓖₂), respectively, such that (M(𝓖₁),τ₁)** is isometrically isomorphic to (M(𝓖₂),τ₂)** if and only if 𝓖₁ and 𝓖₂ are topologically isomorphic. In particular, this leads to a new proof of Ghahramani-Lau's isometrical isomorphism theorem for compact groups, different from those of Ghahramani and J. P. McClure (2006) and Dales et al. (2012).
LA - eng
KW - locally compact groups; measure algebra; generalized functions vanishing at infinity; second dual
UR - http://eudml.org/doc/286150
ER -