论文标题
关于Banach代数的Hermitian元素的功能性演算：标准和光谱半径
On functional calculus for Hermitian elements of Banach algebras: the norm and spectral radius
论文作者
论文摘要
让$ a $为复杂的Unital Banach代数。如果$ \ | \ exp（ita）\ | = 1 $ in r $中的所有$ t \。对于希尔伯特空间中有界线性操作员的代数，这一遗产财产与普通的自我偶然性一致。如果$ a \ in $是Hermitian，则$ | a | = || a || $，其中$ | a | $表示$ a $的频谱半径。如果$ \ || f（a）|| = | f（a）| $ \对于$ a $和所有hermitian $ a \ a $ in a $。我们根据积极的确定函数来表征通用符号。
Let $ A$ be a complex unital Banach algebra. An element $a \in A$ is said to be Hermitian, if $ \| \exp (ita) \| =1$ for all $t\in R$. In the case of the algebra of bounded linear operators in a Hilbert space this Hermitian property agrees with the ordinary selfadjointness. If $a \in A$ is Hermitian, then $|a|=||a||$, where $|a|$ denotes the spectral radius of $a$. A function $F: R\to \C$ is called the universal symbol if $ \|| F(a)||= |F(a)|$\ for each $ A$ and all Hermitian $a\in A$. We characterize universal symbols in terms of positive definite functions.
