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- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms/10.2.129
- Publisher site
- See Article on Publisher Site
Abstract
H. G. DALES CONTENTS 1. Introduction. 129 2. Homomorphisms and derivations. 132 3. Characters and topological algebras. 135 4. The radical and semi-simplicity. 138 5. Algebras of power series. 144 6. Point derivations. 149 7. Some radical algebras. 154 8. Maps from algebras of analytic functions. 159 9. Homomorphisms from C*-algebras. 163 10. Continuity of derivations and homomorphisms: further results. 174 11. Linear functionals. 177 1. Introduction Let 21 and 93 be Banach algebras. The basic automatic continuity problem is to give algebraic conditions on 21 and 93 which ensure that every homomorphism 6: 93 -> 21 is necessarily continuous. More generally, let 21 and 93 be topological vector spaces, and let 6: 23 -> 21 be a linear map such that some further algebraic condition is satisfied: we seek theorems which assert the automatic continuity of 0. For example, if 21 is a Banach algebra and if X is a Banach 2l-bimodule, is every derivation D : 21 -*• X continuous? If X is a Banach space, is every linear operator which commutes with an operator on X of given type necessarily continuous? If 21 is a topological star algebra, is every positive linear functional on 21 necessarily
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Jul 1, 1978