A. Bonilla

activity

20102020

most citedMean Li-Yorke chaos in Banach spaces

46 citations · 96 across the 9 of their papers we have counts for

collaborators

13 papers

math.FA2020★ 2 cited

Zero-one law of orbital limit points for weighted shifts

Antonio Bonilla, Rodrigo Cardeccia, Karl-G. Grosse-Erdmann +1

Chan and Seceleanu have shown that if a weighted shift operator on $ℓ^{p} (Z)$ , $1 \leq p < \infty$ , admits an orbit with a non-zero limit point then it is hypercyclic. We pr…

math.FA2020★ 43 cited

Frequently recurrent operators

Antonio Bonilla, Karl-G. Grosse-Erdmann, Antoni López-Martínez +1

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 partic…

math.FA2019★ 2 cited

Kreiss bounded and uniformly Kreiss bounded operators

A. Bonilla, V. Müller

If $T$ is a Kreiss bounded operator on a Banach space, then $∥ T^{n} ∥ = O (n)$ . Forty years ago Shields conjectured that in Hilbert spaces, $∥ T^{n} ∥ = O (n)$ . A negative answer t…

math.FA2019★ 3 cited

Reiterative distributional chaos on Banach spaces

Antonio Bonilla, Marko Kostić

If we change the upper and lower density in the definition of distributional chaos of a continuous linear operator on Banach space by the Banach upper and Banach lower density, res…

math.FA2018

$C_{0}$ -semigroups of $m$ -isometries on Hilbert spaces

T. Bermudez, A. Bonilla, H. Zaway

Let ${T (t)}_{t \geq 0}$ be a $C_{0}$ -semigroup on a separable Hilbert space $H$ . We characterize that $T (t)$ is an $m$ -isometry for every $t$ in terms that the mapping $t\in \Bbb R^+…

math.FA2018★ 46 cited

Mean Li-Yorke chaos in Banach spaces

N. C. Bernardes, A. Bonilla, A. Peris

We investigate the notion of mean Li-Yorke chaos for operators on Banach spaces. We show that it differs from the notion of distributional chaos of type 2, contrary to what happens…

math.FA2017

Growth orders and ergodicity for absolutely Cesàro bounded operators

Luciano Abadias, Antonio Bonilla

In this paper, we extend the concept of absolutely Cesàro boundedness to the fractional case. We construct a weighted shift operator belonging to this class of operators, and we pr…

math.FA2017

Cesàro bounded operators in Banach spaces

Teresa Bermúdez, Antonio Bonilla, Vladimir Müller +1

We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Cesàro bounded and strong Kreiss bounded (in particular, uniformly…

math.FA2016

Upper frequent hypercyclicity and related notions

Antonio Bonilla, Karl-G. Grosse-Erdmann

Enhancing a recent result of Bayart and Ruzsa we obtain a Birkhoff-type characterization of upper frequently hypercyclic operators and a corresponding Upper Frequent Hypercyclicity…

math.FA2015

Rate of growth of hypercyclic and frequently hypercyclic functions for the Dunkl operator

Luis Bernal-Gonzalez, Antonio Bonilla

For the Dunkl operator $Λ_{α}$ $(α > - 1/2)$ on the space of entire functions on the complex space C, the critical rate of growth for the integral means $M_{p} (f, r)$ of their hypercyclic…

math.CV2015

Order of growth of distributional irregular entire functions for the differentiation operator

Luis Bernal-Gonzalez, Antonio Bonilla

We study the rate of growth of entire functions that are distributionally irregular for the differentiation operator D. More specifically, given $p \in [1, \infty]$ and $b \in (0,a…

math.FA2014

On convex-cyclic operators

T. Bermúdez, A. Bonilla, N. Feldman

We give a Hahn-Banach Characterization for convex-cyclicity. We also obtain an example of a bounded linear operator $S$ on a Banach space with $σ_{p} (S^{*}) = \emptyset$ such that $S$ …

math.FA2010

Li-Yorke and distributionally chaotic operators

T. Bermudez, A. bonilla, F. Martínez-Giménez +1

We study Li-Yorke chaos and distributional chaos for operators on Banach spaces. More precisely, we characterize Li-Yorke chaos in terms of the existence of irregular vectors. Suff…