论文标题
分析功能的加权BergmanFréchet和（LB）空间的CESàRO操作员
The Cesàro operator on weighted Bergman Fréchet and (LB)-spaces of analytic functions
论文作者
论文摘要
CESàRooperator $ \ MATHSF {C} $的频谱是在作为交叉点出现的空间上确定的$ 0 <α<\ infty $。相对于$α$，我们将它们视为加权伯格曼空间$ a^p_α$的投射限制（分别电感限制）。证明这些空间将单一空间作为Schauder基础，为使用Grothendieck-Pietsch标准推断出我们最终以非核Fréchet-Schwartz Space（分别是非核（DFS）-Space）的方式铺平了道路。我们表明，$ \ mathsf {c} $始终是连续的，而$ a^p_^p_ {α+} $和$ a^p_^p_ {α-} $都无法紧凑或不限制逆向。
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 $A^p_{α-}$.
