Arens regularity and point Arens regularity of semigroup algebras
| Autor: | J. Laali, Alireza Medghalchi, Ramin Ramezani |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pointwise
Mathematics::Functional Analysis Pure mathematics 021103 operations research Mathematics::Operator Algebras Semigroup General Mathematics High Energy Physics::Phenomenology 010102 general mathematics 0211 other engineering and technologies 02 engineering and technology Operator theory 01 natural sciences Potential theory Theoretical Computer Science Identity (mathematics) Physics::Space Physics Astrophysics::Solar and Stellar Astrophysics Point (geometry) 0101 mathematics Analysis Mathematics |
| Zdroj: | Positivity. 23:1215-1224 |
| ISSN: | 1572-9281 1385-1292 |
| DOI: | 10.1007/s11117-019-00662-8 |
| Popis: | The purpose of this article is to study the concepts Arens regularity for semigroup algebras $$M_a(S)$$ , $$\ell ^1(S)$$ , and $${ LUC}(S)^*$$ . We give a necessary and sufficient condition for $$M_a(S)$$ to be pointwise Arens regular. We then give some characterizations for Arens regularity of $$M_a(S)$$ and $$\ell ^1(S)$$ . Also, we investigate weakly compact multipliers on $$M_a(S)$$ and then for a compactly cancellative foundation semigroup S with identity, we show that S is compact if $${ LUC}(S)^*$$ is Arens regular. |
| Databáze: | OpenAIRE |
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