Unitary equivalence of invariant subspaces in the polydisk

Kei Ji Izuchi

Vol. 130 (1987), No. 2, 351–358

DOI: 10.2140/pjm.1987.130.351

Abstract

Invariant subspaces M and N of H²(Tⁿ) are called unitarily equivalent if M = ψN for a unimodular function ψ on Tⁿ. In this note, it is given a complete characterization of pairs of invariant subspaces M and N of H²(Tⁿ) such that M = ϕN for an inner function ϕ. This is a generalization of Agrawal, Clark and Douglas’ results. As an application, if M is an invariant subspace of H²(Tⁿ) and if M is unitarily equivalent to S(f), an invariant subspace generated by an outer function f, then M = ϕS(f) for some inner function ϕ.

Mathematical Subject Classification 2000

Primary: 46E15

Secondary: 32A35, 46J15, 47A15, 47B38

Milestones

Received: 12 July 1986

Published: 1 December 1987