On Supercyclicity of Tuples of Operators.

In this paper, we use a result of N. S. Feldman to show that there are no supercyclic subnormal tuples in infinite dimensions. Also, we investigate some spectral properties of hypercyclic tuples of operators. Besides, we prove that if $$T$$ is a supercyclic $$\ell $$ -tuple of commuting $$n\times n$$ complex matrices, then $$\ell \ge n$$ and also there exists a supercyclic $$n$$ -tuple of commuting diagonal $$n\times n$$ matrices. Furthermore, we see that if $$T=(T_{1},\ldots ,T_{n})$$ is a supercyclic $$n$$ -tuple of commuting $$n\times n$$ complex matrices, then $$T_{j}$$ 's are simultaneously diagonalizable. [ABSTRACT FROM AUTHOR]