The following type of question first arose in 1972 work of Kadison and Kastler: If A and B are two algebras of bounded operators on a Hilbert space H which are “sufficiently close”, what properties do they share?

In general, A and B need not be isomorphic, nor must their lattices of invariant subspaces be related. However, when A and B belong to certain classes of operator algebras, good results can be obtained.

In this talk, I will discuss some of these classes and when close algebras belonging to these classes are isomorphic.