Contractively included subspaces of Pick spaces

TL;DR

This paper characterizes specific contractively included subspaces within Pick spaces, extending known results from Hardy, Drury--Arveson, and invariant subspace theories in a unified framework.

Contribution

It provides new characterizations of contractively included subspaces of Pick spaces, generalizing previous results for Hardy and Drury--Arveson spaces.

Findings

Characterizations of contractively included subspaces in Pick spaces

Extension of invariant subspace results to a broader class of spaces

Unified framework for subspace characterization in reproducing kernel Hilbert spaces

Abstract

Pick spaces are a class of reproducing kernel Hilbert spaces that generalize the classical Hardy space and the Drury--Arveson reproducing kernel spaces. We give characterizations of certain contractively included subspaces of Pick spaces. These generalize the characterization of closed invariant subspaces of Trent and McCullough, as well as results for the Drury--Arveson space obtained by Ball, Bolotnikov and Fang.