کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4607591 | 1337871 | 2012 | 29 صفحه PDF | دانلود رایگان |
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 dd-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.This work is a continuation and extension of results presented by Gröchenig and Klotz (2010) [23].
Journal: Journal of Approximation Theory - Volume 164, Issue 2, February 2012, Pages 268–296