Mezban Habibi Babadi - Payam Noor University, P.O. Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran

The paper gives a survey of commutator tuples and infinity tuples of commutative bounded linear mappings on a Hilbert space, also we will investigate the properties of nuclear class of tuples and non-hypercyclic tuples. Let H be an ordered Hilbert space and T1, T2,...Tn are commutative bounded linear operators on H. If T = (T1, T2, ...,Tn) take (.... ). Orbit of h E H under T defined by Orb(t, h) = {Sh: S erT}. The tuple T is called hypercyclic if there is a vector he H such that, the set Orb(T, h) is dense in H. In this case, the vector h is called a hypercyclic vector for T and T is called hypercyclic tuple, the tuple T is hypercyclic if and only if it is topologically transitive. If h is hypercyclic vector for T and(....) be non negative integers, then(....) is hypereyclic vector for T.

Hilbert space, Hypercyclic vector