Derivations with large separating subspace

Author:
C. J. Read

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3671-3677

MSC (2000):
Primary 46H20, 46H05; Secondary 46H40, 13A02, 13A10, 46M05, 13A05

DOI:
https://doi.org/10.1090/S0002-9939-02-06485-7

Published electronically:
April 22, 2002

MathSciNet review:
1920047

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Abstract | References | Similar Articles | Additional Information

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 to itself must map into the radical. The proof goes via first showing that the separating subspace of a derivation on must lie in the radical of . In this paper, we exhibit discontinuous derivations on a commutative unital Fréchet algebra such that the separating subspace is the whole of . Thus, the situation on Fréchet algebras is markedly different from that on Banach algebras.

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Additional Information

**C. J. Read**

Affiliation:
Faculty of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

Email:
read@maths.leeds.ac.uk

DOI:
https://doi.org/10.1090/S0002-9939-02-06485-7

Keywords:
Derivation,
Fr\'{e}chet algebra,
Banach algebra,
radical,
separating subspace,
automatic continuity

Received by editor(s):
March 13, 2001

Received by editor(s) in revised form:
July 24, 2001

Published electronically:
April 22, 2002

Communicated by:
N. Tomczak-Jaegermann

Article copyright:
© Copyright 2002
American Mathematical Society