The main purpose of this paper
is to classify the C∗-algebras of the form A′ + 𝒦, where A′ denotes the commutant of
an abelian von Neumann algebra A, and 𝒦 is the set of compact operators. By the
famous result of Johnson and Parrott, A′ + 𝒦 is the same as the essential
commutant of A. These algebras were studied by Plastiras in the special case in
which A is generated by its minimal projections and in addition all of these
projections are finite dimensional. Using a theorem of Andersen, we are
able to generalize Plastiras’ main results to general abelian von Neumann
algebras. We also study the automorphism groups and derivations of these
algebras.
