Converse of a Theorem of Foias and Reflexive Lattices of Operator Ranges Sing-Cheong Ong Indiana University Mathematics Journal 1981 text pdf 10.1512/iumj.1981.30.30005 10.1512/iumj.1981.30.30005 en Indiana Univ. Math. J. 30 (1981) 57 - 63 state-of-the-art mathematics http://iumj.org/access/