解析函数的加权Bergman Fréchet和（LB）-空间上的Cesàro算子
The Cesàro operator on weighted Bergman Fréchet and (LB)-spaces of analytic functions
摘要：
Cesàro算子$\mathsf{C}$的谱是在作为交叉$A^p_{α+}$（分别是）产生的空间上确定的。对于$0<α<\infty$，由标准径向权$(1-|z|)^α$诱导的$1<p<\infty$阶Bergman空间$A_α^p$的并集$A^p_{α-}$。我们将它们视为简化的投影极限（分别）。归纳极限）的加权Bergman空间$A^p_α$，关于$α$。证明这些空间允许单项式作为Schauder基，为使用Grothendieck-Pietsch准则推断我们最终得到非核Fréchet-Schwartz空间铺平了道路。非核（DFS）空间）。证明了$\mathsf{C}$总是连续的，但它不是紧的，也不是$A^p_{α+}$和$A^p_{α-}$上的有界逆.
英文摘要：
The spectrum of the Cesàro operator $\mathsf{C}$ is determined on the spaces which arises as intersections $A^p_{α+}$ (resp. unions $A^p_{α-}$) of Bergman spaces $A_α^p$ of order $1<p<\infty$ induced by standard radial weights $(1-|z|)^α$, for $0<α<\infty$. We treat them as reduced projective limits (resp. inductive limits) of weighted Bergman spaces $A^p_α$, with respect to $α$. Proving that these spaces admit the monomials as a Schauder basis paves the way for using Grothendieck-Pietsch criterion to deduce that we end up with a non-nuclear Fréchet-Schwartz space (resp. a non-nuclear (DFS)-space). We show that $\mathsf{C}$ is always continuous, while it fails to be compact or to have bounded inverse on $A^p_{α+}$ and $A^p_{α-}$.
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