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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\cal C (\cal H)$\end{document} of all compact operators by a separable commutative C*-algebra are algebraically reflexive. Concerning the possibly most important extensions by the algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $C(\Bbb T)$\end{document} of all continuous complex valued functions on the perimeter of the unit disc, we show that these groups are topologically nonreflexive.