LOCAL DERIVATIONS ON OPERATOR ALGEBRAS

摘要

When attempting to find sufficient conditions for a linear mapping to be a derivation, an obvious candidate is the concept of a local derivation. Local derivations on operator algebras have been investigated in recent papers of Kadison (J. algebra 130 (1990), 494-509) and Larson and Sourour (Proc. Symp. Pure Math. 51 (1990), 187-194). A local derivation eta is a (norm continuous) linear map from an operator algebra A into an A-bimodule, A which agrees with some derivation at each point in the algebra. We shaw that if A is the direct limit of finite dimensional CSL algebras via *-extendable embeddings (e.g., a triangular AF algebra), then a local derivation on A must be a derivation. Further, we show that for many finite dimensional operator algebras, any inner local derivation must be an inner derivation. (C) 1996 Academic Press, Inc. [References: 18]