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. Then the classical Wiener’s lemma can be reformulated as follows: W(Z,Z) is an inverse-closed subalgebra of B(l), the space of all bounded operators on the space l of square-summable sequences. Here a (quasi-)Banach algebra B, which is a subalgebra of A, is called inverse-closed if any A ∈ B with the inverse A ∈ A implies A ∈ B. Wiener’s lemma has various extensions and applications. Define GröchenigSchur class S(Z,Z) by S(Z,Z) := {

WIENER'S LEMMA FOR INFINITE MATRICES OF GOHBERG-BASKAKOV-SJÖSTRAND CLASS