eng Science and Education Publishing American Journal of Mathematical Analysis 2333-8431 2015-06-23 3 2 44 46 10.12691/ajma-3-2-4 AJMA2015324 article On the Construction of Families of type П1 Subfactors Each Containing a Middle Subfactors Bahman Mashood b_mashood@hotmail.com 1 Mahmood Khoshkam 1 Former lecturer at university of Saskatchewan, San Francisco/California In this article we are going to construct a family of type П1 subfactors each containing a middle subfactor. As a result of the above construction we show that the set of the indices of hyperfinite irreducible subfactors contains the interval [37.0037,). http://pubs.sciepub.com/ajma/3/2/4/ajma-3-2-4.pdf subfactors von Neumann algebras Jones Index lattice relative commutants