Zobrazeno 1 - 10
of 27
pro vyhledávání: '"Cardeccia, Rodrigo"'
Autor:
Cardeccia, Rodrigo, Muro, Santiago
We study frequently recurrent unilateral and bilateral backward shift operators on Fr\'echet sequence spaces. We prove that if a backward shift admits a non-zero frequently recurrent vector, then it supports a dense set of such vectors, so that the o
Externí odkaz:
http://arxiv.org/abs/2407.11799
Autor:
Cardeccia, Rodrigo, Muro, Santiago
We prove that reiteratively hypercyclic operators have perfect spectrum. Consequently, it follows that there exist separable infinite dimensional Banach spaces that do not support any reiteratively hypercyclic operator. For this, we study $\mathcal F
Externí odkaz:
http://arxiv.org/abs/2204.13542
Autor:
Cardeccia, Rodrigo
Publikováno v:
Ergod. Th. Dynam. Sys. 44 (2024) 1315-1329
We prove that a finite set of natural numbers $J$ satisfies that $J\cup\{0\}$ is not Sidon if and only if for any operator $T$, the disjoint hypercyclicity of $\{T^j:j\in J\}$ implies that $T$ is weakly mixing. As an application we show the existence
Externí odkaz:
http://arxiv.org/abs/2203.16617
Autor:
Cardeccia, Rodrigo, Muro, Santiago
We study multiply recurrent and hypercyclic operators as a special case of $\mathcal F$-hypercyclicity, where $\mathcal F$ is the family of subsets of the natural numbers containing arbitrarily long arithmetic progressions. We prove several propertie
Externí odkaz:
http://arxiv.org/abs/2104.15033
Chan and Seceleanu have shown that if a weighted shift operator on $\ell^p(\mathbb{Z})$, $1\leq p<\infty$, admits an orbit with a non-zero limit point then it is hypercyclic. We present a new proof of this result that allows to extend it to very gene
Externí odkaz:
http://arxiv.org/abs/2007.01641
Autor:
Cardeccia, Rodrigo, Muro, Santiago
We characterize chaotic linear operators on reflexive Banach spaces in terms of the existence of long arithmetic progressions in the sets of return times. To achieve this, we study $\mathcal F$-hypercyclicity for a family of subsets of the natural nu
Externí odkaz:
http://arxiv.org/abs/2003.07161
Autor:
Cardeccia, Rodrigo
We study the dynamics induced by an $m$-linear operator. We answer a question of B\`es and Conejero showing an example of an $m$-linear hypercyclic operator acting on a Banach space. Moreover we prove the existence of $m$-linear hypercyclic operators
Externí odkaz:
http://arxiv.org/abs/1905.12057
Autor:
Cardeccia, Rodrigo, Muro, Santiago
We study the dynamics induced by homogeneous polynomials on Banach spaces. It is known that no homogeneous polynomial defined on a Banach space can have a dense orbit. We show, a simple and natural example of a homogeneous polynomial with an orbit th
Externí odkaz:
http://arxiv.org/abs/1806.11543
Autor:
Cardeccia, Rodrigo, Muro, Santiago
It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fr\'echet spaces. We show the existence of hypercyclic polynomials on $H(\mathbb C)$,
Externí odkaz:
http://arxiv.org/abs/1703.04773
Autor:
Cardeccia, Rodrigo
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 May 2020 485(1)
