Inverse closedness of approximation algebras |
| |
Authors: | JM Almira U Luther |
| |
Institution: | a Departamento de Matemáticas, Universidad de Jaén, E.U.P. Linares, C/ Alfonso X el Sabio, 28, 23700 Linares (Jaén), Spain b Technische Universität Chemnitz, Fakultät für Mathematik, D-09107 Chemnitz, Germany |
| |
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 l1(Z), the property {ck(f)}∈S (ck(f) being the Fourier coefficients of f) implies the same property for 1/f if f∈C(T) vanishes nowhere on T. |
| |
Keywords: | Approximation spaces Quasi-normed algebras Wiener-type theorems |
本文献已被 ScienceDirect 等数据库收录! |
|