Some Invariant Subspaces in L_H²

Abstract

Let H be a separable Hilbert space and let A be the algebra of continuous functions on the torus T ² which are uniform limits of polynomials in e ^imxe ^iny where

(m,n)∈{(m,0)∈Z ²|m ≥ 0}∪{(m,n)∈Z ²|n ≥ 1}.

For this uniform algebra A, we characterize invariant subspaces of L_H².