Derivations with a hereditary domain, II

• Autorzy: A. R. Villena
• Języki publikacji: EN

Abstrakty

EN

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 $B[B ∩ S(D)]B ⊂ Rad_B(A)$ provided that BAB ⊂ A and $dim(Rad_J(A) ∩ ⋂_{n=1}^∞ B^n) < ∞$, where $Rad_J(A)$ and $Rad_B(A)$ denote the Jacobson and the Baer radicals of A respectively. From this we deduce the closability of partially defined derivations on complex semiprime Banach algebras with appropriate domains. The result applies to several relevant classes of algebras.

Kategorie tematyczne

• 46H40: Automatic continuity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 130
• Numer: 3
• Strony: 275-291

Daty

wydano

1998

otrzymano

1997-10-10

poprawiono

1997-12-22

Twórcy

autor

A. R. Villena

• Departamento de Analisis Matematico, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

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