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 multiplicity which satisfies the 4-cycle interpolation condition, then
there are constants δ, C > 0 such that whenever ℳ is another CSL such
that d(Algℒ,Algℳ) < δ, then there is an invertible operator S such that
SAlgℒS−1=Algℳ and ∥S∥∥S−1∥ < 1 + Cd(Algℒ,Algℳ).
