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Jul 18, 2015 at 20:20 comment added Phoenix87 Ah right, thank you Aaron! Indeed I have considered the compacts but I failed to realise it was a counterexample before your comment.
Jul 18, 2015 at 19:10 comment added Aaron Tikuisis The compact operators is a finite C*-algebra, but there are non-strictly positive elements that are Cuntz equivalent to a strictly positive element. Perhaps if you also ask that A is equal to its Pedersen ideal (in the simple case, equivalently, A is algebraically simple) then the question could have a positive answer.
Jul 18, 2015 at 14:48 history asked Phoenix87 CC BY-SA 3.0