Derivations with a hereditary domain, II
Studia Mathematica, Tome 130 (1998) no. 3, pp. 275-291
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
@article{10_4064_sm_130_3_275_291,
author = {A. Villena},
title = {Derivations with a hereditary domain, {II}},
journal = {Studia Mathematica},
pages = {275--291},
publisher = {mathdoc},
volume = {130},
number = {3},
year = {1998},
doi = {10.4064/sm-130-3-275-291},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-130-3-275-291/}
}
A. Villena. Derivations with a hereditary domain, II. Studia Mathematica, Tome 130 (1998) no. 3, pp. 275-291. doi: 10.4064/sm-130-3-275-291
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