论文标题
某些Banach代数的广义推导
Generalized derivations on certain Banach algebras
论文作者
论文摘要
令$ {\ Mathcal a} $为Banach代数，其属性具有$ \ Mathrm {rad}（{\ Mathcal a}）= {\ rm rann}（{\ rm rann}（{\ Mathcal a}）$和algebra $ {\ Mathcal a}/\ mathrmmath a} $ rad}交换性。我们表明，$ {\ Mathcal a} $ maps $ {\ mathcal a} $的推导成$ {\ rm rad}（{\ Mathcal a}）$。使用此情况，我们确定了$ {\ Mathcal a} $映射$ {\ Mathcal a} $的广义推导到$ {\ rm rad}（{\ Mathcal a}）$时。我们还研究了$ {\ Mathcal a} $的$ k $中央化广义推导。然后，对于$ {\ mathcal a} $的广义推导$（δ，d）$，我们获得了$（δ^2，d^2）$的必要条件，仍然是$ {\ Mathcal a} $的广义推导。主要应用与本地紧凑型组的代数有关。特别是，我们将这些结果推论为离散符合群体的傅立叶代数的双重性，以应用我们的方法。
Let ${\mathcal A}$ be a Banach algebra with the properties that $\mathrm{rad}({\mathcal A})={\rm rann}({\mathcal A})$ and the algebra ${\mathcal A}/\mathrm{rad}({\mathcal A})$ is commutative. We show that a derivation of ${\mathcal A}$ maps ${\mathcal A}$ into ${\rm rad}({\mathcal A})$. Using this, we determine among other things when a generalized derivation of ${\mathcal A}$ maps ${\mathcal A}$ into ${\rm rad}({\mathcal A})$. We also study $k$-centralizing generalized derivations of ${\mathcal A}$. Then, for a generalized derivation $(δ, d)$ of ${\mathcal A}$ we obtain a necessary and sufficient condition for $(δ^2, d^2)$ to be still a generalized derivation of ${\mathcal A}$. The main applications are concerned with the algebras over locally compact groups. In particular, we deduce these results for bidual of Fourier algebras of discrete amenable groups as an application of our approach.
