Reflexivity of the automorphism and isometry groups of the suspension of \({\mathcal B}({\mathcal H})\) (Q1281648)

The paper describes the case when local automorphisms are automorphisms. Namely, let \(H\) be a separable, infinite-dimensional Hilbert space. Consider \(C^*\)-algebras of the form \(A= C_0(X)\otimes B(H)\), where \(X\) is a locally compact Hausdorff space. It is shown that every local automorphism (respectively, every local surjective isometry) of \(A\) is an automorphism (respectively, a surjective isometry).