论文标题
在希尔伯特空间的单位球上，较弱的Bloch型空间上的延长Cesàro构图操作员
Extended Cesàro composition operators on weak Bloch-type spaces on the unit ball of a Hilbert space
论文作者
论文摘要
用$ b_x $表示无限二维复杂的Hilbert Space $X。$ LET $ψ\ in H（b_x），$在单位球上所有holomorphic函数的空间$ b_x，$ b_x，$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ in S（b_x）$ holomorphic self y holomorphic self the Holomorphic自我maps $ b_x $ b_x。 $ Let $C_{ψ, φ}: \mathcal B_ν(B_X)$ (and $ \mathcal B_{ν,0}(B_X)$) $\to \mathcal B_μ(B_X) $ (and $ \mathcal B_{μ,0}(B_X)$) be weighted extended Cesàro operators induced by products of the extended cesàro运算符$c_φ$和整体运算符$t_ψ。$在本文中，我们通过$ c_ {ψ，φ} $的界限和紧凑性，通过$ψ$和$φ$的限制到$ m $ $ $ x $ $ x $ $ m m \ ge2。 $基于这些，我们提供了有限件的必要条件以及足够的条件，$ \ wideTilde {c} _ {ψ，φ} $的（弱）紧凑型在Banach valured holomorphic函数之间的空间之间的（φ} $弱粘合到$ \ \ MATHCAL b_x（b_x）$和$ b_v）$ b_x $ b__ b__ b_____x（b_x）$ b_x（b_x）。 $
Denote by $ B_X $ the unit ball of an infinite-dimensional complex Hilbert space $ X. $ Let $ψ\in H(B_X),$ the space of all holomorphic functions on the unit ball $B_X,$ $φ\in S(B_X)$ the set of holomorphic self-maps of $B_X. $ Let $C_{ψ, φ}: \mathcal B_ν(B_X)$ (and $ \mathcal B_{ν,0}(B_X)$) $\to \mathcal B_μ(B_X) $ (and $ \mathcal B_{μ,0}(B_X)$) be weighted extended Cesàro operators induced by products of the extended Cesàro operator $ C_φ$ and integral operator $T_ψ.$ In this paper, we characterize the boundedness and compactness of $ C_{ψ,φ} $ via the estimates for the restrictions of $ ψ$ and $ φ$ to a $ m$-dimensional subspace of $ X $ for some $ m\ge2. $ Based on these we give necessary as well as sufficient conditions for the boundednees, the (weak) compactness of $ \widetilde{C}_{ψ, φ} $ between spaces of Banach-valued holomorphic functions weak-associated to $ \mathcal B_ν(B_X) $ and $ \mathcal B_μ(B_X). $
