Generalized derivations on some convolution algebras

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“…Also, C * -algebras, semisimple Banach algebras with a bounded approximate identity and Banach algebras with rad(A) = ran(A) satisfy the condition ( ). Under this condition, one can prove the results of [1] for A instead of Banach algebra L ∞ 0 (G) * . In the following, we state some of the important results.…”

“…Then L ∞ (G) * and L ∞ 0 (G) * are Banach algebras with the first Arens product. One can prove that L ∞ (G) * and L ∞ 0 (G) * have right identities [5,9]; for more study see [1,2,[11][12][13][14]. Let M(G) be the measure algebra of G. Then M(G) with the convolution product is a unital Banach algebra and M(G) ∼ = C 0 (G) * , where C 0 (G) is the space of all complexvalued continuous functions on G that vanish at infinity [7].…”

“…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].…”

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

“…Bresar [4] gave a generalization of Herstein's result for semiprime rings. Many attempts were made to study this question for Jordan derivations on Banach algebras [2,4,18]. For example, Sinclair [18] proved that every continuous Joradan derivation on a semisimple Banach algebra is a derivation.…”