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Gogić, Ilja
Linear & multilinear algebra, 06/2021, Letnik: 69, Številka: 8Journal Article
Let A be a ring and a ring endomorphism. A generalized skew (or σ-)derivation of A is an additive map for which there exists a map such that for all . If A is a prime -algebra and σ is surjective, we determine the structure of generalized σ-derivations of A that belong to the cb-norm closure of elementary operators on A; all such maps are of the form for suitable elements a,b,c of the multiplier algebra . As a consequence, if an epimorphism lies in the cb-norm closure of , then σ must be an inner automorphism. We also show that these results cannot be extended even to relatively well-behaved non-prime -algebras like .
