“…In the case of subfactor theory of Jones [15], the lattices of intermediate subfactors with their finiteness were studied in Popa [24], Bisch [1], Watatani [27], Teruya and Watatani [25], Longo [20], Khoshkam and Mashhood [19], Grossman and Jones [10], Grossman and Izumi [9] and Xu [28], for example. In these studies, the · 2 -perturbation technique of von Neumann algebras developed by Christensen [6] are essentially used.…”