Infinity Tuple is an infinity component of commutative bounded linear operators acting on common Ordered Hilbert space H(or Ordered Banach space), as T=(T1,T2,...,Tn,...). By Orbit(T,x) as x is in H we mean that union of orbit of all n-tuples generated by T1,T2,....
Is there any problem if we use T(x) for Supn{T1T2...Tn(x):n in N}