Derivations on group algebras of a locally compact abelian group

The Acceptance of Mobile Health Services by Physicians: The Case of Iran

“…Cusack [5] extended this result to semiprime rings. Sinclair [13] proved that every continuous Jordan derivation of a semisimple Banach algebra is a derivation; for derivations and Jordan derivations on group algebras see [1,2,12]. Jordan left derivations have been introduced and studied by Brešar and Vukman [4].…”

Symmetric bi-derivations and their generalizations on group algebras

“…) • m κ+i− j .If i = κ − 2, then by(11) f (m) • m κ−2 = 0.Hence(10) and(11) reduce to κ j even, j=4κ j f (m) • m κ− j = 0 and ) • m κ+i− j = 0.Continuing this procedure, we obtain f (m) = 0 for all m ∈ L ∞ 0 (G) * and therefore, D = 0. Suppose now that κ is odd.…”

Jordan derivations on the $θ-$Lau products of Banach algebras

“…Here a question arises: when dose the converse hold? In 1957, Herstein [10] proved that every Jordan derivation on a 2-torsion free prime ring is a derivation; see also [1,5,14,15]. Bresar [4] gave a generalization of Herstein's result for semiprime rings.…”