  Using principles of the theory of smoothness spaces we give systematic
constructions of scales of inverse-closed subalgebras of a given Banach algebra
with the action of a d-parameter automorphism group. In particular we obtain
the inverse-closedness of Besov algebras, Bessel potential algebras and
approximation algebras of polynomial order in their defining algebra. By a
proper choice of the group action these general results can be applied to
algebras of infinite matrices and yield inverse-closed subalgebras of matrices
with off-diagonal decay of polynomial order. Besides alternative proofs of
known results we obtain new classes of inverse-closed subalgebras of matrices
with off-diagonal decay .
