Sufficient conditions for the projective freeness of Banach algebras |
| |
Authors: | Alexander Brudnyi Amol Sasane |
| |
Institution: | aDepartment of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada;bMathematics Department, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom |
| |
Abstract: | Let R be a unital semi-simple commutative complex Banach algebra, and let M(R) denote its maximal ideal space, equipped with the Gelfand topology. Sufficient topological conditions are given on M(R) for R to be a projective free ring, that is, a ring in which every finitely generated projective R-module is free. Several examples are included, notably the Hardy algebra H∞(X) of bounded holomorphic functions on a Riemann surface of finite type, and also some algebras of stable transfer functions arising in control theory. |
| |
Keywords: | Projective free ring Banach algebra Maximal ideal space |
本文献已被 ScienceDirect 等数据库收录! |
|