GB*-Algebras associated with inductive limits of Hilbert spaces
We investigate a new type of generalized derivations associated with Hochschild 2-cocycles which was introduced by A. Nakajima. We show that every generalized Jordan derivation of this type from CSL algebras or von Neumann algebras into themselves is a generalized derivation under some reasonable conditions. We also study generalized derivable mappings at zero point associated with Hochschild 2-cocycles on CSL algebras.
Let be the triangular algebra consisting of unital algebras and over a commutative ring with identity and be a unital -bimodule. An additive subgroup of is said to be a Lie ideal of if . A non-central square closed Lie ideal of is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on , every generalized Jordan triple higher derivation of into is a generalized higher derivation of into .
In this paper, we investigate a new type of generalized derivations associated with Hochschild 2-cocycles which is introduced by A.Nakajima (Turk. J. Math. 30 (2006), 403–411). We show that if is a triangular algebra, then every generalized Jordan derivation of above type from into itself is a generalized derivation.