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• # Artykuł - szczegóły

## Studia Mathematica

2002 | 151 | 3 | 247-264

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

EN

### Abstrakty

EN
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.

247-264

wydano
2002

### Twórcy

autor
• Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, Canada N9B 3P4