| Résume |
What is the general form of lattice isomorphisms between projection
lattices of von Neumann algebras? In 1930s, von Neumann gave an answer
to this question for type II_1 factors. He proved that a lattice
isomorphism can be described by means of a ring isomorphism between the
algebras of affiliated operators. However, apparently no answer to this
question has been given for the general case (in particular for type III
von Neumann algebras) until now. In this talk, I give an answer to this
question for general von Neumann algebras (save types I_1 and I_2) using
ring isomorphisms between the algebras of locally measurable operators. |
