“…The converse problem, which has been studied for more than 50 years, is to describe Jordan ideals in terms of associative ideals, and to find conditions under which a non-zero Jordan ideal is in fact an associative ideal, or at least it contains a non-zero ideal. For a few references, see [2,3,27,12,13,28,29,7] and the literature therein. Among other papers, Oliveira in [27] showed that a weakly closed Jordan ideal in a nest algebra, which satisfies certain conditions, is an associative ideal.…”