摘要
对于区域Ω上的解析函数f及含单位元的复Banach代数A中的元素a(σ(a) Ω),利用极限引入A上的有界线性算子Df(a),给出了算子Df(a)的积分表示及范数与谱半径的估计;研究了算子Df(a)与内导子δa的关系,证明了δf(a)=Df(a)δa=δaDf(a);讨论了映射αa:f｜→Df(a)的性质,证明了映射αa是从交换Banach代数H(Ω)到算子代数B(A)中的有界线性映射.
For an analytic function f on a region Ω and an element a in a complex Banach algebra A with unit (σ(a)Ω), a bounded linear operator Df(a) on A is introduced. An integral representation of operator Df(a) and an estimation of its norm as well as its spectral radius are established. The relationship between Df(a) and δa is obtained and it is proved that δf(a)=Df(a)δa=δaDf(a) for all f∈H(Ω) and a∈A with σ(a)Ω. Finally, some properties of the map αa:f|→Df(a) are discussed and it is also proved that αa is a bounded linear mapping from H(Ω) into B(A).
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2003年第3期5-8,共4页
Journal of Shaanxi Normal University：Natural Science Edition
基金
国家自然科学基金资助项目(19771056)
陕西省自然科学基金资助项目(2002A02)
