Derivations with a hereditary domain, II
Studia Mathematica, Tome 130 (1998) no. 3, pp. 275-291
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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.
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
@article{10_4064_sm_130_3_275_291,
author = {A. Villena},
title = {Derivations with a hereditary domain, {II}},
journal = {Studia Mathematica},
pages = {275--291},
year = {1998},
volume = {130},
number = {3},
doi = {10.4064/sm-130-3-275-291},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-130-3-275-291/}
}
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