Norms of Basic Operators in Vector Valued Model Spaces and de Branges Spaces

Let $$\Omega _+$$ be either the open unit disc or upper half plane right plane. In this paper, we compute norm of basic operator $$A_\alpha =\Pi _\Theta T_{b_\alpha }|_{\mathcal {H}(\Theta )}$$ in vector valued model space $$\mathcal )=H^m_2 \ominus \Theta H^m_2$$ associated with an $$m\times m$$ matrix inner function $$\Theta $$ and show that is attained. Here $$\Pi denotes orthogonal projection from Lebesgue $$L^m_2$$ onto )$$ $$T_{b_\alpha }$$ multiplication by elementary Blaschke factor $$b_{\alpha degree one a zero at point $$\alpha \in \Omega . We if strictly contractive, then its may expressed terms singular values (\alpha extend evaluation to more general setting de Branges spaces.