On existence of finite universal Korovkin sets in the centre of group algebras (Q676833)

The problem of characterizing commutative Banach algebras possessing finite universal Korovkin systems is still open in general. In 1990, M. Pannenberg showed that if \(G\) is a locally compact abelian group, then \(L^1(G)\) admits a finite universal Korovkin system iff the dual group of \(G\) is a finite dimensional separable metric space. In this paper, the compact groups \(G\) as well as connected central topological groups \(G\) for which the centre \(Z(L^1(G))\) possess a finite universal Korovkin system are characterized. Other related results are also obtained.