Reflexivity of the automorphism and isometry groups of C*-algebras in BDF theory

We prove that the automorphism and isometry groups of any extension of the C-algebra l(H) of all compact operators by a separable commutative C*-algeb ra are algebraically reflexive. Concerning the possibly most important exte nsions by the algebra C(T) of all continuous complex valued functions on th e perimeter of the unit disc, we show that these groups are topologically n onreflexive.