“…Recall that the joint left essential spectrum o¡e(Tx, ... , Tn) of Tx, ... , TN is defined as the joint left spectrum of 7r(70, ..., n(TN) . Let us recall (see [KP,Lemma 2.1]) that X = (Xx, ... , Xfi) £ oie(Tx, ... , 7jv), if and only if there exists an orthonormal sequence {xn} such that lim,,-^ \\(T¡ -A,)jc"|| = 0, for i = I, ... , N. Moreover, using standard techniques we can prove Lemma 1.1. Let Tx, ... ,Tn be commuting operators on ß?…”