Mezban Habibi Babadi - PhD student at PNU, Shiraz, Iran Genaveh Branch, Islamic Azad University, Genaveh, Iran
S. Nasrin Hosseini Monfared - Department of Mathematics Genaveh Branch, Islamic Azad University, Genaveh, Iran

In this paper, will investigate characterize the Chaotically Conditions for the Tuples of special commutative bounded mapping, acting on Banach spaces. Suppose X be an Fsequence space whit the unconditional basis k k N e  { } and let n T , T , T ,... T 1 2 3are unilateral weighted backward shifts with weight sequences k k N e  { } 1, ,k k N e  { } 2 ,, …,n k k N e  { } ,and( , , ,..., ) 1 2 3 n T  T T T T be a tuple of operators n T , T , T ,... T 1 2 3 . Then T is chaotic if and onlyif T is Hypercyclic and has a non-trivial periodic point if and only if T has a non-trivialperiodic point if and only if the series      1 11,1mmkk m e e ,       1 11, 2mmkk m e e , …,        1 11,mmkk n m e eare convergence in X .

Tuples of operators, Hilbert Schmidt Tuples, Hypercyclicity, Infinity Tuples