### A structure theory for Jordan ${H}^{*}$-pairs

Jordan ${H}^{*}$-pairs appear, in a natural way, in the study of Lie ${H}^{*}$-triple systems ([3]). Indeed, it is shown in [4, Th. 3.1] that the problem of the classification of Lie ${H}^{*}$-triple systems is reduced to prove the existence of certain ${L}^{*}$-algebra envelopes, and it is also shown in [3] that we can associate topologically simple nonquadratic Jordan ${H}^{*}$-pairs to a wide class of Lie ${H}^{*}$-triple systems and then the above envelopes can be obtained from a suitable classification, in terms of associative ${H}^{*}$-pairs, of...