We use the free entropy defined by D. Voiculescu to prove that the free group factors cannot be decomposed as closed linear spans of noncommutative monomials in elements of nonprime subfactors or abelian * -subalgebras, if the degrees of monomials have an upper bound depending on the number of generators. The resulting estimates for the hyperfinite and abelian dimensions of free group factors settle in the affirmative a conjecture of L. Ge and S. Popa (for infinitely many generators).
Abstract. In this paper we prove that any II 1 -subfactor of finite index in the interpolated free group factor L(Ft) is prime for any 1 < t ≤ ∞ i.e., it is not isomorphic to tensor products of II 1 -factors.
Every meromorphic function on C with doubly periodic phase is equal to an elliptic function multiplied by a meromorphic function determined by the periods.
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