Derivations with large separating subspace

Read, C.

doi:10.1090/S0002-9939-02-06485-7

Derivations with large separating subspace
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by C. J. Read PDF

Proc. Amer. Math. Soc. 130 (2002), 3671-3677 Request permission

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 Fréchet algebra $\mathcal {A}$ such that the separating subspace is the whole of $\mathcal {A}$. Thus, the situation on Fréchet algebras is markedly different from that on Banach algebras.

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