Bi-derivations and quasi-multipliers on module extensions Banach algebras
| Autor: | Ali Jabbari, Ali Ebadian |
|---|---|
| Jazyk: | English<br />Portuguese |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Boletim da Sociedade Paranaense de Matemática, Vol 41 (2022) |
| Druh dokumentu: | article |
| ISSN: | 0037-8712 2175-1188 |
| DOI: | 10.5269/bspm.52574 |
| Popis: | This paper characterize two bi-linear maps bi-derivations and quasi-multipliers on the module extension Banach algebra $A\oplus_1 X$, where $A$ is a Banach algebra and $X$ is a Banach $A$-module. Under some conditions, it is shown that if every bi-derivation on $A\oplus_1 A$ is inner, then the quotient group of bounded bi-derivations and inner bi-derivations, is equal to space of quasi-multipliers of $A$. Moreover, it is proved that $\mathrm{QM}(A \oplus_1 A)=\mathrm{QM}(A)\oplus (\mathrm{QM}(A)+\mathrm{QM}(A)')$, where $\mathrm{QM}(A)'=\{m\in \mathrm{QM}(A):m(0,a)=m(a,0)=0\}$. |
| Databáze: | Directory of Open Access Journals |
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