tailieunhanh - Báo cáo toán học: "On the computation of invariants for ITPFI factors "

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Trên tính toán bất biến cho các yếu tố ITPFI. | J. OPERATOR THEORY 15 1986 83 107 Copyright by INCREST 1986 ON THE COMPUTATION OF INVARIANTS FOR ITPFI FACTORS T. GIORDANO G. SKANDAL1S E. J. WOODS Krieger s theorem 11 states in part that the flow of weights considered as a mapping from type TII0 Krieger factors see terminology with algebraic isomorphism as the equivalence relation to strictly ergodic flows with conjugacy as the equivalence relation is one-to-one and onto between equivalence classes. The simplest flows are the pure point spectrum flows 5 . The corresponding Krieger factors are known to be 1TPF1 4 and the motivation for the present work was to obtain explicit eigenvalue list constructions of these factors. This problem leads naturally to the construction of Section 1 where we introduce an invariant T see below which can be computed much more easily than the flow of weights and seems to be very useful. The main result of this section is Theorem which is basic for Section 2 and is also used in Sections 3 and 4. This invariant can be understood in terms of the flow of weights as follows see Remark . Let M be a factor Í2 p F itsflow of weights and T a subgroup of the Conncs invariant T M which is also the L -point spectrum of Q p F . Let older be a multiplicative choice of eigenfunctions of Í2 p Ft . This gives a map ÍÌ - T given by a 0 fe ò . The measure P defines a certain equivalence class r A T of measures on T see Proposition . The relation with the original problem is as follows. Let M be a Krieger factor and take T T M . Then the flow of weights will be a pure point spectrum flow iff the map f is essentially injective and the Haar measure on T belongs to i M T . in 8 Hamachi and Osikawa consider the 1TPF12 factors M Lk k 0 2 1 and prove that for Lk sufficiently large the flow of weights is pure point spectrum. In Section 3 we study this family of factors. We compute for all sequences Lk the flow of weights by showing that the map indicated above is essentially injective Theorem