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Let $𝔐$ be a Jordan-Banach algebra with identity 1, whose norm satisfies: (i) $\parallel ab\parallel \le \parallel a\parallel \parallel b\parallel$,   $a,b\in 𝔐$ (ii) $\parallel a^2\parallel =\parallel a{\parallel }^2$ (iii) $\parallel a^2\parallel \le \parallel a^2+b^2\parallel$. $𝔐$ is called a JB algebra (E.M. Alfsen, F.W. Shultz and E. Stormer, Oslo preprint (1976)). The set ${𝔐}^{+}$ of squares in $𝔐$ is a closed convex cone. $(𝔐,{𝔐}^{+},\mathbf{1})$ is a complete ordered vector space with $\mathbf{1}$ as a order unit. In addition, we assume $𝔐$ to be monotone complete (i.e. $𝔐$ coincides with the bidual ${𝔐}^{**}$),...