Abstract
Local derivations and automorphisms on operator algebras have been investigated in recent papers of Kadison, and Larson-Sourour. A local derivation η is a (norm continuous) linear map from an operator algebra A into an A-bimodule M so that for each A in A there is a derivation δ from A into M with η(A) = δ[A](A). We say that a local derivation is inner if each δ[A] can be chosen to be inner for each A in A . We show that local derivations on finite dimensional CSL algebras must be derivations, extending a result of Kadison to a wide class of finite dimensional non-self-adjoint algebras. Further, we show that if the local derivation is inner, then it must be an inner derivation. The first result is then extended to triangular AF algebras, which are direct limit algebras formed from certain types of finite dimensional CSL algebras. We also characterize local automorphisms on finite dimensional CSL algebras.
Crist, Randall Lee (1993). Local mappings of operator algebras. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -1517813.