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Derivations with large separating subspace
- Source :
- Proceedings of the American Mathematical Society. 130:3671-3677
- Publication Year :
- 2002
- Publisher :
- American Mathematical Society (AMS), 2002.
-
Abstract
- In his famous paper The image of a derivation is contained in the radical, Marc Thomas establishes the (commutative) Singer-Wermer conjecture, showing that derivations from a commutative Banach algebra A to itself must map into the radical. The proof goes via first showing that the separating subspace of a derivation on A must lie in the radical of A. In this paper, we exhibit discontinuous derivations on a commutative unital Frechet algebra A such that the separating subspace is the whole of A. Thus, the situation on Frechet algebras is markedly different from that on Banach algebras.
Details
- ISSN :
- 10886826 and 00029939
- Volume :
- 130
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society
- Accession number :
- edsair.doi...........7a57b192e8c10b052e4c73aea2128c7b