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Sep 4, 2010 at 21:25 comment added Andreas Thom That is true. What is meant is that the positive square-root (which exists in $C(S^1)$) does not lie in $\ell^1 {\mathbb Z}$. Otherwise, I think that Riesz proved that every non-negative Laurent polynomial is a hermitian square (or maybe sum of such squares).
Sep 4, 2010 at 13:58 comment added Rasmus @Andreas: Regarding 4): Isn't $2-z-z^{-1}=(1-z^{-1})(1-z)=(1-z)^*(1-z)$?
Sep 2, 2010 at 19:14 history edited Andreas Thom CC BY-SA 2.5
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Sep 2, 2010 at 6:30 history answered Andreas Thom CC BY-SA 2.5