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Aug 27, 2015 at 8:11 comment added Simon Henry Then ok. I was asking because you only said "$K_0(A)$ and $K_1(A)$ to agree with... " so I wasn't sure you wanted anything about the $K_n$ for $n \geqslant 2$.
Aug 27, 2015 at 7:47 comment added Jonathan Gleason Would bott periodicity not simply follow from the fact that the higher $K$-groups also agree with ordinary operator $K$-theory?
Aug 27, 2015 at 7:43 comment added Simon Henry Do you also want that the Higher $K_n$ satifies bott periodicity for $C^*$-algebra ? or just that the first two group agrees ?
Aug 26, 2015 at 18:00 comment added Jonathan Gleason Sorry, that was my mistake. I said $K_0$, but I really meant $K_\bullet$. That is, I want $K_0(A)$ and $K_1(A)$ to agree with $K_0^{\text{op}}(A)$ and $K_1^{\text{op}}(A)$ to agree for $A$ a $C^*$-algebra. The question has been edited accordingly.
Aug 26, 2015 at 16:21 history answered Simon Henry CC BY-SA 3.0