Summary: Jones Index theory for type II von
Departamento de Matem´atica
Facultad de Ciencias Exactas
Universidad Nacional de La Plata
(1900) La Plata
R. Longo's definition of index ([L2]) is extended to the case where the in-
volved algebras are not factors, assuming they are of type II. Main tools are
generalizations of technics used by R. Longo. It is shown that our definition
agrees with that of Baillet, Denizeau and Havet for von Neumann algebras,
and also that it is equivalent to the one given in [AS] by E. Andruchow y D.
Stojanoff. We obtain some properties about the tower and the tunnel of the
inclusion. Also the techniques involved allow us to prove some known results,
generally straightforwardly. Results obtained are applied to inclusion of type
III von Neumann algebras with separable predual.