Derivations with a hereditary domain, II

Villena, A.

Villena, A.

Studia Mathematica, Tome 129 (1998), p. 275-291 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $B [B \cap S (D)] B \subset R a d_{B} (A)$ provided that BAB ⊂ A and $d i m (R a d_{J} (A) \cap ⋂_{n = 1}^{\infty} B^{n}) < \infty$ , where $R a d_{J} (A)$ and $R a d_{B} (A)$ 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.

Publié le : 1998-01-01

Zbl 0918.46048

EUDML-ID : urn:eudml:doc:216558

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     author = {A. Villena},
     title = {Derivations with a hereditary domain, II},
     journal = {Studia Mathematica},
     volume = {129},
     year = {1998},
     pages = {275-291},
     zbl = {0918.46048},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv130i3p275bwm}
}

Villena, A. Derivations with a hereditary domain, II. Studia Mathematica, Tome 129 (1998) pp. 275-291. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv130i3p275bwm/

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