On the Banach space isomorphism type of AF C*-algebras and their triangular subalgebras

It is shown that all the approximately finite dimensional C^*-algebras which are not of Type I are isomorphic as Banach spaces. This generalizes the matroid case given previously by Arazy. Analogous results are obtained for various families of triangular subalgebras of AF C^*-algebras. In addition the classification of various continua of Type I AF C^*-algebras is discussed.