Sums of squares in real analytic rings

Fernando, José

doi:10.1090/S0002-9947-02-02956-2

Sums of squares in real analytic rings
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by José F. Fernando PDF

Trans. Amer. Math. Soc. 354 (2002), 1909-1919 Request permission

Abstract:

Let $A$ be an analytic ring. We show: (1) $A$ has finite Pythagoras number if and only if its real dimension is $\leq 2$, and (2) if every positive semidefinite element of $A$ is a sum of squares, then $A$ is real and has real dimension $2$.

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