Dual pairs techniques in H*-theories Original Research Article

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−), left angle bracket right-pointing angle bracket) is an associative pair such that ((R+, R−)J,) with x, y, z := left angle bracketx, y, zright-pointing angle bracket + left angle bracketz, y, xright-pointing angle bracket 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 RJ.