On Hilbert Schmidt Tuples of Operators and Chaotically Condition

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 .

Keywords:

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