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 H 2.