论文标题
在连续功能及其子空间的空间上加权组成的半群
Weighted composition semigroups on spaces of continuous functions and their subspaces
论文作者
论文摘要
本文专用于连续函数及其子空间空间上的加权组成半群。我们考虑由班克空间上的半流量和半循环引起的半群，在Hausdorff空间上连续功能的$ \ MATHCAL {F}（ω）$，使得Norm-Topology比紧凑型拓扑更强大，例如紧凑型拓扑，例如Hardy Space and the the the the the the the the the the dirich dirich dirich dirich dirich dirich dirich dirich dirich dirich dirich dirich dirich dirich dirich dirich dirich dirich dirich空间连续或塑形功能的空间。 Gallardo-Gutiérrez，Siskakis和Yakubovich表明，在Banach空间上没有非平凡的规范性连续的加权组成半群，$ \ Mathcal {f}（\ Mathbb {d}）$ holomorphic $ holomorphic $ holomorphic to holomorphic to holomorphic在开放的单位disc $ \ mathb $ \ mathbb} $ {d} $ {d} $ {d} $ h^{\ infty} \ subset \ mathcal {f}（\ mathbb {d}）\ subset \ subset \ mathcal {b} _ {1} $其中$ h^{\ infty} $是在$ \ \ mathbb {d d} $ farmy holomorphic函数上的硬性空间$ \ MATHCAL {B} _ {1} $ Bloch Space。但是，我们表明，这些空间上有非平凡的加权组成半群，这些空间是强烈连续的W.R.T.标准 - 拓扑与紧凑型拓扑之间的混合拓扑结构。我们在连续功能的Banach空间的一般环境中研究了这种加权组成的半群，并在所涉及的空间中得出了必要的和足够的条件，对于强连续性W.R.T.混合拓扑和作为规范连续性的副产品。此外，我们给出了其发电机及其规范连续性空间的几种特征。
This paper is dedicated to weighted composition semigroups on spaces of continuous functions and their subspaces. We consider semigroups induced by semiflows and semicocycles on Banach spaces $\mathcal{F}(Ω)$ of continuous functions on a Hausdorff space $Ω$ such that the norm-topology is stronger than the compact-open topology like the Hardy spaces, the weighted Bergman spaces, the Dirichlet space, the Bloch type spaces, the space of bounded Dirichlet series and weighted spaces of continuous or holomorphic functions. It was shown by Gallardo-Gutiérrez, Siskakis and Yakubovich that there are no non-trivial norm-strongly continuous weighted composition semigroups on Banach spaces $\mathcal{F}(\mathbb{D})$ of holomorphic functions on the open unit disc $\mathbb{D}$ such that $H^{\infty}\subset\mathcal{F}(\mathbb{D})\subset\mathcal{B}_{1}$ where $H^{\infty}$ is the Hardy space of bounded holomorphic functions on $\mathbb{D}$ and $\mathcal{B}_{1}$ the Bloch space. However, we show that there are non-trivial weighted composition semigroups on such spaces which are strongly continuous w.r.t. the mixed topology between the norm-topology and the compact-open topology. We study such weighted composition semigroups in the general setting of Banach spaces of continuous functions and derive necessary and sufficient conditions on the spaces involved, the semiflows and semicocycles for strong continuity w.r.t. the mixed topology and as a byproduct for norm-strong continuity as well. Moreover, we give several characterisations of their generator and their space of norm-strong continuity.
