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A new order relation for JB-algebras. (English) Zbl 0808.46072

For a Jordan ring for which \(2x= 0\) only if \(x=0\), define \(x\leq y\) iff \(xy= x^ 2\), \(x^ 2 y= xy^ 2= x^ 3\). The author gives conditions for \(\leq\) to be a partial order; in particular, this is so for a JB- algebra.

MSC:

46H70 Nonassociative topological algebras
17C65 Jordan structures on Banach spaces and algebras
06A06 Partial orders, general
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References:

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