论文标题
在弱的全态空间上加权构图算子，并应用于希尔伯特空间的单位球上的弱蓝色型空间
Weighted composition operators on weak holomorphic spaces and application to weak Bloch-type spaces on the unit ball of a Hilbert space
论文作者
论文摘要
让$ e $成为单位球上的全体形态功能的空间banach $y。$ $我们建立了界限，加权组成算子的（弱）紧凑性$ w_ {ψ，φ}：f \ mapstoψ\ cdot（f \ circumcirccφ）$ on $ e $和$ e $和$ \ widetilde { $ on $ we（y）$通过分开的子空间$w。$作为应用程序的某些特征，通过估计$ψ$和$φ$的限制和$ m $ x $ x $ $ x $的$ m \ ge2的$ \ ge2 $，我们表征了上面提到的$ w_ w_的$ w_ c {ψ， b_μ（b_x）$ holomorphic函数在单位球上$ b_x $ b_x $的无限维二维型希尔伯特空间及其关联的空间$ w \ mathcalb_μ（b_x，y），其中$μ$在$ b_x上是正常的重量。 $
Let $ E $ be a space of holomorphic functions on the unit ball $ B_X $ of a Banach space $ X.$ In this work, we introduce a Banach structure associated to $ E $ on the linear space $ WE(Y) $ containing $ Y$-valued holomorphic functions on $ B_X $ such that $ w \circ f \in E $ for every $ w \in W, $ a separating subspace of the dual $ Y' $ of a Banach $ Y. $ We establish the relation between the boundedness, the (weak) compactness of the weighted composition operators $ W_{ψ,φ}: f\mapsto ψ\cdot(f \circ φ) $ on $ E $ and $ \widetilde{W}_{ψ,φ}: g\mapsto ψ\cdot(g \circ φ) $ on $ WE(Y)$ via some characterizations of the separating subspace $ W. $ As an application, via the estimates for the restrictions of $ ψ$ and $ φ$ to a $ m$-dimensional subspace of $ X $ for some $ m\ge2, $ we characterize the properties mentioned above of $ W_{ψ,φ} $ on Bloch-type spaces $ \mathcal B_μ(B_X) $ of holomorphic functions on the unit ball $ B_X $ of an infinite-dimensional Hilbert space as well as their the associated spaces $W\mathcal B_μ(B_X,Y), $ where $ μ$ is a normal weight on $ B_X. $
