J-Class Abelian Semigroups of Matrices on Cn and Hypercyclicity
Abstract
We give a characterization of hypercyclic finitely generated abelian semigroups of matrices on Cn using the extended limit sets (the J-sets). Moreover we construct for any n≥ 2 an abelian semigroup G of GL(n;C) generated by n + 1 diagonal matrices which is locally hypercyclic but not hypercyclic and such that JG(ek) = Cn for every k = 1; : : : ; n, where (e1; : : : ; en) is the canonical basis of Cn. This gives a negative answer to a question raised by Costakis and Manoussos.
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