Reflexivity of the automorphism and isometry groups of the suspension of $B(H)$

Abstract

The aim of this paper is to show that the automorphism and isometry groups of the suspension of $B(H)$, $H$ being a separable infinite dimensional Hilbert space, are algebraically reflexive. This means that every local automorphism, respectively local surjective isometry of $C_0(\mathbb{R})\otimes B(H)$ is an automorphism, respectively a surjective isometry.