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Derivations on Jordan-Banach algebras

A. Villena (1996)

Studia Mathematica

We establish that all derivations on a semisimple Jordan-Banach algebra are automatically continuous. By showing that "almost all" primitive ideals in the algebra are invariant under a given derivation, the general case is reduced to that of primitive Jordan-Banach algebras.

Derivations with a hereditary domain, II

A. Villena (1998)

Studia Mathematica

The nilpotency of the separating subspace of an everywhere defined derivation on a Banach algebra is an intriguing question which remains still unsolved, even for commutative Banach algebras. On the other hand, closability of partially defined derivations on Banach algebras is a fundamental problem motivated by the study of time evolution of quantum systems. We show that the separating subspace S(D) of a Jordan derivation defined on a subalgebra B of a complex Banach algebra A satisfies B [ B S ( D ) ] B R a d B ( A ) provided...

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