Algebry operatorów i ich zastosowania w fizyce

We consider a new class of potentially exotic group C*-algebras C*(PF_p*(G)) for a locally compact group G, and its connection with the class of potentially exotic group C*-algebras C*_{L^p}(G) introduced by Brown and Guentner. Surprisingly, these two classes of C*-algebras are intimately related. By exploiting this connection, we show C*_{L^p}(G)=C*(PF_{p}*(G)) for p>2, and the C*-algebras C*_{L^p}(G) are pairwise distinct for p>2 when G belongs to a large class of nonamenable groups possessing the Haagerup property and either the rapid decay property or Kunze-Stein phenomenon by characterizing the positive definite functions that extend to positive linear functionals of C*_{L^p}(G) and C*(PF_{p}*(G)). This greatly generalizes earlier results of Okayasu and Wiersma on the pairwise distinctness of C*_{L^p}(G) for p>2 when G is either a noncommutative free group or the group SL(2,R), respectively. This is based on a joint work with M. Wiersma.