J-Class Abelian Semigroups of Matrices on C^n and Hypercyclicity

Details J-Class Abelian Semigroups of Matrices on C^n and Hypercyclicity J-Class Abelian Semigroups of Matrices on C^n and Hypercyclicity

2011-05-07

arxiv.org/abs/1105.1473v1

Mathematics

Functional Analysis

10 pages

Scientific paper

We give a characterization of hypercyclic finitely generated abelian semigroups of matrices on C^n using the extended limit sets (the J-sets). Moreover we construct for any n\geq 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(e_k) = C^n for every k = 1; : : : ; n, where (e_1; : : : ; e_n) is the canonical basis of C^n. This gives a negative answer to a question raised by Costakis and Manoussos.

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