Minimal determinants of topological centres for some algebras associated with locally compact groups
Bulletin of the London Mathematical Society, cilt.43, sa.3, ss.495-506, 2011 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 43 Sayı: 3
- Basım Tarihi: 2011
- Doi Numarası: 10.1112/blms/bdq116
- Dergi Adı: Bulletin of the London Mathematical Society
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.495-506
- Boğaziçi Üniversitesi Adresli: Evet
Özet
The second dual L1(G)** of the group algebra has a well-known Arens multiplication (μ, ν) μν which is weak* continuous in the μ variable. In contrast, if ν μν is weak* continuous at every point, then μ ∈ L1(G). A significant question is whether continuity at all points ν is necessary for this conclusion, and there has been a long-standing conjecture that continuity at just two specified points might be enough. The main conclusion of the present paper is that the minimal number is in fact just one. However, a second theorem considers a closely related question for which two points are required. The methods yield similar answers to corresponding problems about the quotient algebra LUC(G)* of L1(G)** and the compactification GLUC of the group G. © 2011 London Mathematical Society.