On operators which commute with analytic Toeplitz operators modulo the finite rank operators

摘要

It is shown that an operator S on the Hardy space H-2(D-n) (or H-2(B-n)) commutes with all analytic Toeplitz operators modulo the finite rank operators if and only if S = T-g + F. Here F is a finite rank operator, and in the case n = 1, g is a sum of a rational function and a bounded analytic function, and in the case n >= 2, g is a bounded analytic function.