光谱距离诱导生长特性的应用
Applications of the Growth Characteristics Induced by the Spectral Distance
摘要：
设$A$是复单位巴拿赫代数.利用谱距离与某一整映射的增长特性之间的联系，将其转化为$A$，得到了Gelfand著名的幂有界性定理的一个推广.在详细阐述这些思想的基础上，借助下调和函数的Phragmen-Lindelöf方法，作为主要结果，证明了$C^*$ -代数的两个正规元素相等当且仅当它们是拟幂零等价的。
英文摘要：
Let $A$ be a complex unital Banach algebra. Using a connection between the spectral distance and the growth characteristics of a certain entire map into $A$, we derive a generalization of Gelfand's famous Power Boundedness Theorem. Elaborating on these ideas, with the help of a Phragmén-Lindelöf device for subharmonic functions, it is then shown, as the main result, that two normal elements of a $C^*$-algebra are equal if and only if they are quasinilpotent equivalent.
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