The operator-valued Poisson kernel and its applications (original) (raw)

This paper presents the operator-valued Poisson kernel, focusing on its properties and applications within operator theory and harmonic analysis. It aims to make the subject accessible to non-specialists while exploring the kernel's similarities to the classical Poisson kernel. The work includes a detailed analysis of a dilation-free proof of von Neumann's inequality and the existence of elementary spectral measures for contractions, as well as discussions on functional calculus and the invariant subspace problem.