Existence, automatic continuity and invariant submodules of generalized derivations on modules
The authors first show that free modules and projective modules always have nontrivial generalized derivations. Then they prove that every minimal prime submodule of a left \(\mathcal A\)-module \(\mathcal{M}\), where \(\mathcal A\) is a \(\mathbb C\)-algebra, is invariant under every generalized derivation. Furthermore, the authors obtain analogs of Posner's theorem for generalized derivations. In the case when \(\mathcal{A}\) is a Banach algebra and \(\mathcal{M}\) is a Banach left \(\mathcal{A}\)-module, the authors study the existence of continuous generalized derivations and automatic continuity of generalized derivations.
scientific article; zbMATH DE number 6109265
scientific article