Invariant subspaces of Brownian shifts on vector-valued Hardy spaces

TL;DR

This paper characterizes invariant subspaces of Brownian shifts on vector-valued Hardy spaces and solves the unitary equivalence problem for these subspaces, advancing understanding of their structure.

Contribution

It provides a complete characterization of invariant subspaces and addresses the unitary equivalence problem for Brownian shifts on vector-valued Hardy spaces.

Findings

Invariant subspaces are fully characterized.

Unitary equivalence problem is solved.

Results extend classical shift theory to vector-valued Hardy spaces.

Abstract

We characterize invariant subspaces of Brownian shifts on vector-valued Hardy spaces. We also solve the unitary equivalence problem for the invariant subspaces of these shifts.