Inductive extreme non-Arens regularity of the Fourier algebra A(G)

Zhiguo Hu. "Inductive extreme non-Arens regularity of the Fourier algebra A(G)." Studia Mathematica 151.3 (2002): 247-264. <http://eudml.org/doc/284587>.

@article{ZhiguoHu2002,
abstract = {Let G be a non-discrete locally compact group, A(G) the Fourier algebra of G, VN(G) the von Neumann algebra generated by the left regular representation of G which is identified with A(G)*, and WAP(Ĝ) the space of all weakly almost periodic functionals on A(G). We show that there exists a directed family ℋ of open subgroups of G such that: (1) for each H ∈ ℋ, A(H) is extremely non-Arens regular; (2) $VN(G) = ⋃_\{H∈ℋ\} VN(H)$ and $VN(G)/WAP(Ĝ) = ⋃_\{H∈ℋ\} [VN(H)/WAP(Ĥ)]$; (3) $A(G) = ⋃_\{H∈ℋ\} A(H)$ and it is a WAP-strong inductive union in the sense that the unions in (2) are strongly compatible with it. Furthermore, we prove that the family A(H): H ∈ ℋ of Fourier algebras has a kind of inductively compatible extreme non-Arens regularity.},
author = {Zhiguo Hu},
journal = {Studia Mathematica},
keywords = {-algebras; non-Arens regularity; Fourier algebra; locally compact group},
language = {eng},
number = {3},
pages = {247-264},
title = {Inductive extreme non-Arens regularity of the Fourier algebra A(G)},
url = {http://eudml.org/doc/284587},
volume = {151},
year = {2002},
}

TY - JOUR
AU - Zhiguo Hu
TI - Inductive extreme non-Arens regularity of the Fourier algebra A(G)
JO - Studia Mathematica
PY - 2002
VL - 151
IS - 3
SP - 247
EP - 264
AB - Let G be a non-discrete locally compact group, A(G) the Fourier algebra of G, VN(G) the von Neumann algebra generated by the left regular representation of G which is identified with A(G)*, and WAP(Ĝ) the space of all weakly almost periodic functionals on A(G). We show that there exists a directed family ℋ of open subgroups of G such that: (1) for each H ∈ ℋ, A(H) is extremely non-Arens regular; (2) $VN(G) = ⋃_{H∈ℋ} VN(H)$ and $VN(G)/WAP(Ĝ) = ⋃_{H∈ℋ} [VN(H)/WAP(Ĥ)]$; (3) $A(G) = ⋃_{H∈ℋ} A(H)$ and it is a WAP-strong inductive union in the sense that the unions in (2) are strongly compatible with it. Furthermore, we prove that the family A(H): H ∈ ℋ of Fourier algebras has a kind of inductively compatible extreme non-Arens regularity.
LA - eng
KW - -algebras; non-Arens regularity; Fourier algebra; locally compact group
UR - http://eudml.org/doc/284587
ER -