论文标题
标量频谱运算符和半群的光谱包含和映射定理
On spectral inclusion and mapping theorems for scalar type spectral operators and semigroups
论文作者
论文摘要
我们为标量频谱运算符建立光谱包含和映射定理，从而推广其对应器的正常运算符。因此，我们将精确的弱频谱映射定理扩展到复杂的希尔伯特空间上的普通运算符的$ C_0 $ - 元素，并在复杂的$ C_0 $ -Semigroup上的标量频谱运算符的更通用的情况下，在复杂的Banach Space上。较细的频谱结构被逐项考虑。
We establish spectral inclusion and mapping theorems for scalar type spectral operators, generalizing their counterparts for normal operators. Thereby, we extend a precise weak spectral mapping theorem, known to hold for $C_0$-semigroups of normal operators on complex Hilbert spaces, to the more general case of $C_0$-semigroups of scalar type spectral operators on complex Banach spaces. The finer spectrum structure is given itemized consideration.
