论文标题
离散群体的全身代数的歼灭者
Annihilators in the bidual of generalized group algebra of a discrete group
论文作者
论文摘要
简而言之，研究了配备了两种Arens产品的全身群体代数$（\ ell^1（g，\ \ Mathcal a），\ ast）$，其中$ g $是任何离散的群体，$ \ \ mathcal a $ as $ as $ is是一个包含$（\ ell^1 bunter）的Banach代数，该代数包含$（\ ell^1（\ elt）$（\ el^1（\ elt）。我们在代数$ \ ell^1（g，\ mathcal a）^{**} $中给出了一个明确的an灭家族（w.r.t a arens产品），是由$ \ mathbb n $且不在拓扑中心的$ \ mathbb n $引起的。结果，我们还推断出$ \ ell^1（g，\ mathcal a）$并非强烈不规则。
In this short note, the second dual of generalized group algebra $(\ell^1(G,\mathcal A),\ast)$ equipped with both Arens products is investigated, where $G$ is any discrete group and $\mathcal A$ is a Banach algebra containing a complemented algebraic copy of $(\ell^1(\mathbb N),\bullet)$. We give an explicit family of annihilators(w.r.t both the Arens product) in the algebra $\ell^1(G,\mathcal A)^{**}$, arising from non-principal ultrafilters on $\mathbb N$ and which are not in the topological center. As a consequence, we also deduce the fact that $\ell^1(G,\mathcal A)$ is not Strongly Arens irregular.
