A REMARK ON THE MINIMAL INDEX OF SUBFACTORS

Let M {superset double equals} N be a factor-subfactor pair with a faithful normal conditional expectation E: M → N satisfying Ind E < + ∞. Let N {subset double equals} M {subset double equals} M1 {subset double equals} M2 ··· be the Jones tower of basic extensions, and Ek: Mk → Mk - 1 be the dual expectation constructed canonically from the given E. We prove that, if E: M → N is minimal, then so is the composition E ° E1 ° ··· ° Ek: Mk → N. Some consequences of this result are also presented. © 1992.