Topology Proceedings 33 (2009), pp. 185-196

Extreme non-Arens regularity of semigroup algebras

Mahmoud Filali and Tero Vedenjuoksu

Let S be an infinite, discrete, weakly cancellative semigroup, l^∞(S) the space of bounded functions on S, and WAP(S) the subspace of weakly almost periodic functions. Then the quotient space l^∞(S)/WAP(S) contains an isometric linear copy of l^∞(S). This implies that the semigroup algebra l¹(S) is extremely non-Arens regular.

Keywords: extreme non-Arens regular, weakly almost periodic, slowly oscillating functions, semigroup algebra

Mathematics Subject Classification: 43A20, 43A10(22A15)

Document formats: PDF file 183.7 Kb

Topology Proceedings, Volume 33 (2009)
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