Bounded point derivations on certain Banach algebras
Bounded point derivations on certain Banach algebras
复制标题
某些 Banach 代数的有界点导数
DOI：
10.1016/0022-1236(67)90025-0
复制
发表时间：
1967
影响因子：
1.7
通讯作者：
J. Wermer
中科院分区：
文献类型：
--
作者：
J. Wermer
设X是z平面上的紧集。用R (X)表示X上没有极点的所有有理函数的代数，设R (X)是X上一致范数中R (X)的闭包，则R (X)是该范数中的Banach代数。众所周知，R (X)在标量中的同态都是-+ f (X)的形式，其中X是X中的某个点，我们将X点与它诱导的同态识别。在x中固定x，很容易验证在x处存在有界点导数当且仅当
Let now X be a compact set in the z-plane. Denote by R,(X) the algebra of all rational functions having no poles on X. Let R (X) be the closure of R,(X) in the uniform norm on X. R (X) is then a Banach algebra in this norm.It is well known that the homomorphisms of R (X) into the scalars are all of the formf-+ f ( x), wh ere x is some point in X. We identify the point x with the homomorphism it induces. Fix x in X. It is easy to verify that there exists a bounded point derivation at x if and only if