Abstract. The aim of this paper is to show that the automorphism and isometry groups of the infinite direct sum $\ell_\infty({\msbm N}, {\cal B}({\cal H}))$ of operator algebras are topologically reflexive which, as one of our former results shows, is not the case with the ``scalar algebra" $\ell_\infty $.

AMS Subject Classification (1991): 47B49, 46L40, 47D25 54D35

Keyword(s): Reflexivity, automorphism group, isometry group, operator algebra, Stone-Čech compactification

Received October 13, 1997 and in revised form March 16, 1998. (Registered under 3315/2009.)