Hypercyclic bilinear operators on Banach spaces

被引：2

作者：

Cardeccia, Rodrigo ^{[1
,2
]}

机构：

[1] Univ Buenos Aires, Fac CS Exactas & Nat, Dept Matemat PAB 1, RA-1428 Buenos Aires, DF, Argentina

[2] Consejo Nacl Invest Cient & Tecn, IMAS, Buenos Aires, DF, Argentina

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 485卷 / 10期

关键词：

Hypercyclic multilinear operators; Dense orbits; Bihypercyclic bilinear operators; Multilincar operators; CHAOTIC POLYNOMIALS;

D O I：

10.1016/j.jmaa.2019.123771

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the dynamics induced by an m-linear operator. We answer a question of Bes 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 on arbitrary infinite dimensional separable Banach spaces. We also prove an existence result about symmetric bihypercyclic bilinear operators, answering a question by Grosse-Erdmann and Kim. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：20

共 21 条

[1] [Anonymous], [No title captured]
[2] [Anonymous], 1952, Journal d'Analyse Mathematique, DOI DOI 10.1007/BF02786968
[3] Existence of hypercyclic operators on topological vector spaces
Ansari, SI
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 148 (02) : 384 - 390
[4] Chaotic polynomials in spaces of continuous and differentiable functions
Aron, Richard M.
Miralles, Alejandro
[J]. GLASGOW MATHEMATICAL JOURNAL, 2008, 50 : 319 - 323
[5] Bayart F, 2009, CAMB TRACT MATH, P1, DOI 10.1017/CBO9780511581113
[6] On hypercyclic operators on Banach spaces
Bernal-González, L
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (04) : 1003 - 1010
[7] Bernardes N. C., 1998, QUAEST MATH, V21, P311
[8] An Extension of Hypercyclicity for N-Linear Operators
Bes, Juan
Conejero, J. Alberto
[J]. ABSTRACT AND APPLIED ANALYSIS, 2014,
[9] Birkhoff GD, 1929, CR HEBD ACAD SCI, V189, P473
[10] Hypercyclic operators on non-normable Frechet spaces
Bonet, J
Peris, A
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 159 (02) : 587 - 595

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