States on unital partially-ordered groups. (English) Zbl 1265.06052

Summary: We study states on unital po-groups which are not necessarily commutative as normalized positive real-valued group homomorphisms. We show that in contrast to the commutative case, there are examples of unital po-groups having no state. We introduce the state interpolation property holding in any abelian unital po-group, and we show that it holds in any normal-valued unital \(\ell \)-group. We present a connection among states and ideals of po-groups, and we describe extremal states on the state space of unital po-groups.


06F15 Ordered groups
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