Abstract
This work is a version for Jordan pairs, of a previous result for Jordan algebras given in Rodriguez (1988). However, the tools we use are completely different from those in Rodriguez (1988). A Jordan H ∗- pair is (in a sense) a complicated algebraic object enriched with a Hilbert space structure which is well related to its algebraic structure. In this work we describe a certain class of Jordan H ∗- pairs by forgetting their Hilbert space structure and starting with the remaining purely algebraic information available on it. More precisely, if (( R +, R −), 〈 〉) is an associative pair such that (( R +, R −) J ,) with x, y, z := 〈 x, y, z〉 + 〈 z, y, x〉 is a topologically simple Jordan H ∗- pair , then R can be endowed of an (associative) H ∗- pair structure such that its H ∗- symmetrized agrees with the Jordan H ∗- pair R J .
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