Mixing and weakly mixing abelian subalgebras of type II<inf>1</inf> factors

This paper studies weakly mixing (singular) and mixing masas in type II1 factors from a bimodule point of view. Several necessary and sufficient conditions characterizing the normalizing algebra of a masa are presented. We study the structure of mixing inclusions, with special attention paid to masas of product class. A recent result of Jolissaint and Stalder concerning mixing masas arising out of inclusions of groups is revisited. One consequence of our structural results rules out the existence of certain Koopman-realizable measures arising from semidirect products which are absolutely continuous, but not Lebesgue. We also show that there exist uncountably many pairwise non-conjugate mixing masas in the free group factors each with Pukánszky invariant {1,∞}.