Distributional chaos for operators with full scrambled sets

作者：Martinez Gimenez Felix; Oprocha Piotr; Peris Alfredo^*

来源：Mathematische Zeitschrift, 2013, 274(1-2): 603-612.

DOI：10.1007/s00209-012-1087-8

• Distributional chaos
• Hypercyclic operators
• Irregular vectors

In this article we answer in the negative the question of whether hypercyclicity is sufficient for distributional chaos for a continuous linear operator (we even prove that the mixing property does not suffice). Moreover, we show that an extremal situation is possible: There are (hypercyclic and non-hypercyclic) operators such that the whole space consists, except zero, of distributionally irregular vectors.

• 出版日期2013-6