I'm reading secondary literature where they make this claim, however, I cannot see why it holds true. This is a reformulation from a previous question that I didn't specify good enough.

  • $\begingroup$ What is A? What does it mean to take p(a) where p is a pure state and a is an algebra element? How do you define ||a||? You need to be much more specific and rigorous. $\endgroup$ – oleg Sep 6 '19 at 15:36
  • $\begingroup$ Reading which literature? $\endgroup$ – Qmechanic Sep 6 '19 at 16:12
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    $\begingroup$ $A$ is the $C$*-algebra. And $||$ $||$ is the norm. That should be obvious. $\endgroup$ – Annonymus Sep 6 '19 at 17:30
  • $\begingroup$ @Annonymus Please edit the original question, rather than reposting it as a new one. When you edit the original, it will put it into a queue for people to decide if it should be reopened or not. $\endgroup$ – tpg2114 Sep 8 '19 at 16:48