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

• Autorzy: Zhiguo Hu
• Języki publikacji: 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.

Kategorie tematyczne

• 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
• 22D25: C * -algebras and W * -algebras in relation to group representations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 151
• Numer: 3
• Strony: 247-264

Daty

wydano

2002

Twórcy

autor

Zhiguo Hu

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

Identyfikatory

DOI

10.4064/sm151-3-4