论文标题
抽象乘法运算符的基本光谱，规范和光谱半径
The essential spectrum, norm, and spectral radius of abstract multiplication operators
论文作者
论文摘要
让$ e $成为一个复杂的Banach晶格，$ t $是Centrum $ z（e）= \ {t：| t | t | \leλi\ mbox {for Some}λ\} $的运算符。那么$ t $的基本规范$ \ | | | _ {e} $等于$ t $的基本频谱半径$ r_ {e}（t）$。我们还证明了$ r_ {e}（t）= \ max \ {\ | t_ {a^{a^{d}} \ |，r_ {e}（t_ {a}）\} $，其中$ t_ {a} $是$ t $ and $ t $ and $ t $ and $ t $ and $ t $ and $ t_ {a^a^$ nont nont and nont and nont and此外，$ r_ {e}（t_ {a}）= \ limsup _ {\ Mathcal f}λ_{a} $，其中$ \ Mathcal f $是$ e $ e $ e $ e $ e $ e $ e} $ e} a} $ e}的$ a $ e} a} a $ e}的$ a a $ a a $ a} a} a = a} a = a} a = a}的fréchet过滤器$ a \ in $。
Let $E$ be a complex Banach lattice and $T$ is an operator in the centrum $Z(E)=\{T: |T|\le λI \mbox{ for some } λ\}$ of $E$. Then the essential norm $\|T\|_{e}$ of $T$ equals the essential spectral radius $r_{e}(T)$ of $T$. We also prove $r_{e}(T)=\max\{\|T_{A^{d}}\|, r_{e}(T_{A})\}$, where $T_{A}$ is the atomic part of $T$ and $T_{A^{d}}$ is the non-atomic part of $T$. Moreover $r_{e}(T_{A})=\limsup_{\mathcal F}λ_{a}$, where $\mathcal F$ is the Fréchet filter on the set $A$ of all positive atoms in $E$ of norm one and $λ_{a}$ is given by $T_{A}a=λ_{a}a$ for all $a\in A$.
