PERTURBATIONS OF CERTAIN REFLEXIVE ALGEBRAS

In this note we use cohomological techniques to prove that if there is a linear map between two CSL algebras which is close to the identity, then the two CSL algebras are similar. We use our result to show that if L is a purely atomic, hyperreflexive CSL with uniform infinite mul tiplicity which satisfies the 4-cycle interpolation condition, then th ere are constants delta, C > 0 such that whenever M is another CSL suc h that d(AlgL, AlgM) < delta, then there is an invertible operator S s uch that SAlgLS-1 = AlgM and \\S\\ \\S-1\\ < 1 + Cd(AlgL, AlgM) .