For $A$ a C* algebra the uniform topology in $Aut(A)$ is defined in terms of neighborhoods for every $a_1$ in $A$

$N(α_1,δ)=[α: ‖α_1∘α^{-1} ‖<δ]$


$‖α‖=[sup⁡{‖α(f)‖/‖f‖ ;f∈A,‖f‖≠0}].$

(Note: the square brackets should be curly)

Is this correct? Any bibliographical reference?

  • $\begingroup$ There's no $a_1$ in your definitions. $\endgroup$ – Martin Argerami Sep 3 '18 at 2:08
  • $\begingroup$ For any automorphism $\alpha\in Aut(A)$, we have $\|\alpha\|=1$ (in fact, $\alpha$ is an isometry). Thus $N(\alpha_1,\delta)=\varnothing$ if $\delta\leq1$ and $=Aut(A)$ if $\delta>1$. This doesn't seem to generate a useful topology on $Aut(A)$. $\endgroup$ – Aweygan Sep 3 '18 at 17:37

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