Rolewicz-type chaotic operators

被引：7
作者：
Bongiorno, D. [1 ]
Darji, U. B. [2 ]
Di Piazza, L. [3 ]
机构：
[1] Univ Palermo, Dipartimento Energia Ingn Informaz & Modelli Mate, Palermo, Italy
[2] Univ Louisville, Dept Math, Louisville, KY 40292 USA
[3] Univ Palermo, Dipartimento Matemat & Informat, I-90123 Palermo, Italy
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 431卷 / 01期
关键词：
Chaotic operators; Hypercyclic operators; Lineable; Rolewicz operator; TOPOLOGICAL VECTOR-SPACES; HYPERCYCLIC OPERATORS; DISTRIBUTIONAL CHAOS; SETS; SPACEABILITY; LINEABILITY;
D O I：
10.1016/j.jmaa.2015.05.073
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article we introduce a new class of Rolevvicz-type operators in l(p), 1 <= p < infinity. We exhibit a collection F having the cardinality of the continuum, consisting of operators of this type which are chaotic and remain so under almost all finite linear combinations, provided that the linear combination has sufficiently large norm. As a corollary to our main result we also obtain that there exists a countable collection of such operators whose all finite linear combinations are chaotic provided that they have sufficiently large norm. (C) 2015 Published by Elsevier Inc.
引用
收藏
页码：518 / 528
页数：11
相关论文
共 22 条
  • [1] Existence of hypercyclic operators on topological vector spaces
    Ansari, SI
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 148 (02) : 384 - 390
  • [2] Lineability and spaceability of sets of functions on R
    Aron, R
    Gurariy, VI
    Seoane, JB
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (03) : 795 - 803
  • [3] Algebrability of the set of non-convergent Fourier series
    Aron, Richard M.
    Perez-Garcia, David
    Seoane-Sepulveda, Juan B.
    [J]. STUDIA MATHEMATICA, 2006, 175 (01) : 83 - 90
  • [4] ON DEVANEY DEFINITION OF CHAOS
    BANKS, J
    BROOKS, J
    CAIRNS, G
    DAVIS, G
    STACEY, P
    [J]. AMERICAN MATHEMATICAL MONTHLY, 1992, 99 (04) : 332 - 334
  • [5] Bayart P., 2009, CAMBRIDGE TRACTS MAT, V179
  • [6] Li-Yorke and distributionally chaotic operators
    Bermudez, T.
    Bonilla, A.
    Martinez-Gimenez, F.
    Peris, A.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 373 (01) : 83 - 93
  • [7] On hypercyclic operators on Banach spaces
    Bernal-González, L
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (04) : 1003 - 1010
  • [8] Lineability criteria, with applications
    Bernal-Gonzalez, Luis
    Ordonez Cabrera, Manuel
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (06) : 3997 - 4025
  • [9] LINEAR SUBSETS OF NONLINEAR SETS IN TOPOLOGICAL VECTOR SPACES
    Bernal-Gonzalez, Luis
    Pellegrino, Daniel
    Seoane-Sepulveda, Juan B.
    [J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 51 (01) : 71 - 130
  • [10] Distributional chaos for linear operators
    Bernardes, N. C., Jr.
    Bonilla, A.
    Mueller, V.
    Peris, A.
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 265 (09) : 2143 - 2163
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