On a class of model Hilbert spaces

Abstract

A detailed description of the model Hilbert space$L^2(\mathbb{R}; d\Sigma; K)$, where $K$ represents a complex,separable Hilbert space, and $\Sigma$ denotes a bounded operator-valued measure,is provided. In particular, we show that several alternative approaches to such a constructionin the literature are equivalent. These spaces are of fundamental importance in the context of perturbation theoryof self-adjoint extensions of symmetric operators, and the spectral theory of ordinary differential operators with operator-valued coefficients.