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

Zhiguo Hu

Zhiguo Hu

Studia Mathematica, Tome 151 (2002), p. 247-264 / Harvested from The Polish Digital Mathematics Library

Résumé

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) $V N (G) = ⋃_{H \in ℋ} V N (H)$ and $V N (G) / W A P (G ̂) = ⋃_{H \in ℋ} [V N (H) / W A P (H ̂)]$ ; (3) $A (G) = ⋃_{H \in ℋ} A (H)$ 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.

Publié le : 2002-01-01

Zbl 1004.22002

EUDML-ID : urn:eudml:doc:284587

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     title = {Inductive extreme non-Arens regularity of the Fourier algebra A(G)},
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     volume = {151},
     year = {2002},
     pages = {247-264},
     zbl = {1004.22002},
     language = {en},
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Zhiguo Hu. Inductive extreme non-Arens regularity of the Fourier algebra A(G). Studia Mathematica, Tome 151 (2002) pp. 247-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-3-4/