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Supporting sequences of pure states on JB algebras

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We show that any sequence $(φ_n)$ of mutually orthogonal pure states on a JB algebra A such that $(φ_n)$ forms an almost discrete sequence in the relative topology induced by the primitive ideal space of A admits a sequence $(a_n)$ consisting of positive, norm one, elements of A with pairwise orthogonal supports which is supporting for $(φ_n)$ in the sense of $φ_n(a_n)=1$ for all n. Moreover, if A is separable then $(a_n)$ can be taken such that $(φ_n)$ is uniquely determined by the biorthogonality condition $φ_n(a_n)=1$. Consequences of this result improving hitherto known extension theorems for C*-algebras and descriptions of dual JB algebras are given.
Słowa kluczowe
  • Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, Technicka 2, 166 27 Praha 6, Czech Republic
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