CHAPTER 4 v CONSTRUCTION OF M NOTATION. Let for every a! G M', r G E, / G H: ( J V ) / ) ^ y) = c ( ^ 2/ » yW(y)c(x, y, y)~xf{x, y) c(z, T ~ V T~ly)-lf(x, r _ 1 y) Then I'(a'),n'(T) G # ( # ) . Moreover, 7r'(r) is unitary. NOTATION. Let M v be the von Neumann algebra generated by I'(af) and 7r(r) for all a' G M'', r G E. Theorem 4.1 Every operator in M v commutes with every operator in M. PROOF. It is enough to check that for a G M, a' G M', r, cr G E: /(a) and 7r(r) commute with I'(a') and 7r'(cr). It can be checked by the straight calculation. • 6

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 1997 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.