[EN] We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Cesaro bounded and strongly Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do ...
Bonet Solves, José Antonio; Bonilla, Antonio(Springer Verlag (Germany), 2013-02-11)
Motivated by recent work on the rate of growth of frequently hypercyclic entire functions due to Blasco, Grosse-Erdmann and Bonilla, we investigate conditions to ensure that the differentiation operator is chaotic or ...
We characterize distributional chaos for linear operators on Fréchet spaces in terms of a computable condition (DCC), and also as the existence of distributionally irregular vectors. A sufficient condition for the existence ...
[EN] Four notions of distributional chaos, namely DC1, DC2, DC21/2 and DC3, are studied within the framework of operators on Banach spaces.. It is known that, for general dynamical systems, DC1 subset of DC2 subset of ...
[EN] An example of a weakly ergodic 3-isometry is provided in [3], we give new examples of weakly ergodic 3-isometries and study numerically hypercyclic m-isometries on finite and infinite dimensional Hilbert spaces. In ...
[EN] Motivated by a recent investigation of Costakis et al. on the notion of recurrence in linear dynamics, we study various stronger forms of recurrence for linear operators, in particular that of frequent recurrence. We ...
We obtain new characterizations of Li Yorke chaos for linear operators on
Banach and Fréchet spaces. We also offer conditions under which an operator admits a
dense set or linear manifold of irregular vectors. Some of ...