# A Beurling-Lax-Halmos theorem for spaces with a complete Nevanlinna-Pick factor

## TL;DR

This paper extends the Beurling-Lax-Halmos theorem to certain reproducing kernel Hilbert spaces with a complete Nevanlinna-Pick factor, including factorization results for nested invariant subspaces.

## Contribution

It provides a new proof of the theorem for these spaces and introduces factorization results for pairs of nested invariant subspaces.

## Key findings

- Establishes a Beurling-Lax-Halmos theorem for spaces with a complete Nevanlinna-Pick factor
- Provides factorization results for pairs of nested invariant subspaces
- Offers a concise proof approach for the theorem

## Abstract

We provide a short argument to establish a Beurling-Lax-Halmos theorem for reproducing kernel Hilbert spaces whose kernel has a complete Nevanlinna-Pick factor. We also record factorization results for pairs of nested invariant subspaces.