We use the free entropy defined by D. Voiculescu to prove that the free group factors can not 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… (More)
We obtain an estimate of Voiculescu's (modified) free entropy dimension for generators of a II 1-factor M with a subfac-tor N containing an abelian subalgebra A of finite multiplicity. It implies in particular that the interpolated free group subfactors of finite Jones index do not have abelian subalgebras of finite multi-plicity or Cartan subalgebras.
Doctoral degree in Microbiology, thesis title: " Researches concerning the effect of rhizospheric microbiota on growth and development of some crop plants " ,
We obtain an estimate of free entropy of generators in a type II 1