On The Topological Center Problem For Certain Banach Algebras From Abstract Harmonic Analysis
Bibliographic record
Abstract
This thesis discusses Banach algebras arising from abstract harmonic analysis and the topological center problems related to them.Let G be a locally compact group.We start with determining the topological center of L 1 pGq.We present two general Banach algebra approaches to tackle this problem.The first approach shows the strong Arens irregularity of the algebra L 1 pGq when G is compact.The second approach shows that the same conclusion still holds when G is non-compact.Indeed, the first approach shows that any weakly sequentially complete Banach algebra that has a bounded approximate identity and is a two-sided ideal in its bidual is strongly Arens irregular; the second approach determines, more generally, the topological centers of the Beurling algebras L 1 pG, q 2 and LU CpG, 1q 1 , with a mild assumption on the weight function .Lastly, the second approach shows the strong Arens irregularity of M pGq for some specific groups.i
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| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
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| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.000 |
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