A unified approach to the topological centre problem for certain Banach algebras arising in abstract harmonic analysis

By M. Neufang. 2002

58 citations recorded by the source corpus.

Abstract.Let $$ \cal G $$ be a locally compact group. Consider the Banach algebra $$ L_{1}(\cal G)^{**} $$ , equipped with the first Arens multiplication, as well as the algebra LUC $$ (\cal G)^* $$ , the dual of the space of bounded left uniformly continuous functions on $$ \cal G $$ , whose product extends the convolution in the measure algebra M $$ (\cal G) $$ . 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 $$ L_{1}(\cal G) $$ and M $$ (\cal G) $$ , 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eaa74f604a896bad9e6480b24c62f44a134886aa

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In Applied Mathematics

1. H. Garth Dales
2. Dona Strauss
3. M. Eshaghi Gordji
4. Anthony To-Ming Lau
5. Mahmoud Filali

In Mathematical Physics

1. Dona Strauss
2. Anthony To-Ming Lau
3. H. Garth Dales
4. M. Eshaghi Gordji
5. Mahmoud Filali
6. M. S. Monfared

Citations in the corpus

• Arens regularity of module actions (2007, background): “We know that for every locally compact group G, the group algebra L1(G) is left strongly Arens irregular (see [13], [9], [15]).”
• Banach Algebras on Semigroups and on Their Compactifications (2010, methodology): “A different proof in the abelian case is given by Ghahramani and McClure in [52], and a proof of a generalization of this theorem is given by Neufang in [110].”