A unified approach to the topological centre
problem for certain Banach algebras arising in abstract harmonic analysis |
| |
Authors: | Email author" target="_blank">M?NeufangEmail author |
| |
Institution: | (1) School of Mathematics and Statistics, Carleton University, K1S 5B6 Ottawa, Ontario, Canada |
| |
Abstract: | Let
be a locally compact group. Consider the Banach algebra
, equipped with the first Arens multiplication, as well as the
algebra LUC
, the dual of the space of bounded left uniformly
continuous functions on
, whose product extends the convolution in
the measure algebra M
. We present (for the most interesting case
of a non-compact group) completely different - in particular,
direct - proofs and even obtain
sharpened versions of
the results, first proved by Lau-Losert in 9] and Lau in
8], that the topological centres of the latter algebras
precisely are
and M
, respectively. The special interest of
our new approach lies in the fact that it shows a fairly general pattern
of solving the topological centre problem for various kinds of Banach
algebras; in particular, it avoids the use of any measure theoretical
techniques. At the same time, deriving both results in perfect
parallelity, our method reveals the nature of their close relation.Received: 1 January 2002 |
| |
Keywords: | 22D15 43A20 43A22 |
本文献已被 SpringerLink 等数据库收录! |
|