Luther, Uwe ; Almira, Jose Maria : Inverse Closedness of Approximation Algebras

Author(s):

Luther, Uwe
Almira, Jose Maria

Title:

Inverse Closedness of Approximation Algebras

Electronic source:

application/pdf
application/postscript

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 19, 2004

Mathematics Subject Classification:

41A65			[ Abstract approximation theory ]
46J30			[ Subalgebras ]

Abstract:

We prove the inverse closedness of certain approximation algebras based on a quasi-Banach algebra X using two general theorems on the inverse closedness of subspaces of quasi-Banach algebras. In the first theorem commutative algebras are considered while the second theorem can be applied to arbitrary X and to subspaces of X which can be obtained by a general K-method of interpolation between X and an inversely closed subspace Y of X having certain properties. As application we present some inversely closed subalgebras of C(T) and C[-1,1]. In particular, we generalize Wiener's theorem, i.e., we show that for many subalgebras S of l^1(Z), the property {c_k(f)}\in S (c_k(f) being the Fourier coefficients of f) implies the same property for 1/f if f\in C(T) vanishes nowhere on T.

Keywords:

Approximation spaces, Quasi-normed algebras, Wiener-type theorems

Language:

English

Publication time:

12 / 2004