论文标题
矢量有价值的模型空间和de branges空间中基本运算符的规范
Norms of basic operators in vector valued model spaces and de Branges spaces
论文作者
论文摘要
令$ω_+$为开放单元盘或开放的上半平面或右半平面。在本文中，我们计算基本运算符的规范$a_α=π_θT_{b_α} | _ {\ Mathcal {h}（H}（θ）（θ）} $在矢量型号$ \ MATHCAL {h}（θ）（θ）= h^m_2 \ am_2 $ $ m_2 $ in $ m_2 $ m y $ m Mathcal {h}（θ） $ω_+$，并表明已达到规范。这里$π_θ$表示lebesgue space的正交投影$ l^m_2 $ to $ \ mathcal {h}（θ）$和$ t_ {b_α} $是基本blaschke factor $b_α$ a y ose a in a in a in point $ n $yα$的乘法的乘法运算符。我们表明，如果$a_α$严格承担，那么它的标准可以用$θ（α）$的单数值表示。然后，我们将此评估扩展到更通用的矢量有价值de Branges空间。
Let $Ω_+$ be either the open unit disc or the open upper half plane or the open right half plane. In this paper, we compute the norm of the basic operator $A_α=Π_ΘT_{b_α}|_{\mathcal{H}(Θ)}$ in the vector valued model space $\mathcal{H}(Θ)=H^m_2 \ominus ΘH^m_2$ associated with an $m\times m$ matrix valued inner function $Θ$ in $Ω_+$ and show that the norm is attained. Here $Π_Θ$ denotes the orthogonal projection from the Lebesgue space $L^m_2$ onto $\mathcal{H}(Θ)$ and $T_{b_α}$ is the operator of multiplication by the elementary Blaschke factor $b_α$ of degree one with a zero at a point $α\in Ω_+$. We show that if $A_α$ is strictly contractive, then its norm may be expressed in terms of the singular values of $Θ(α)$. We then extend this evaluation to the more general setting of vector valued de Branges spaces.
