In this article, we present several equivalent conditions ensuring the disjoint supercyclicity of finite weighted pseudo-shifts acting on an arbitrary Banach sequence space. The disjoint supercyclic properties of weighted translations on locally compact discrete groups, the direct sums of finite classical weighted backward shifts, and the bilateral backward operator weighted shifts can be viewed as special cases of our main results. Furthermore, we exhibit an interesting fact that any finite bilateral weighted backward shifts on the space l2(Z) never satisfy the d-Supercyclicity Criterion by a simple proof.
Ya WANG
,
Yu-Xia LIANG
. DISJOINT SUPERCYCLIC WEIGHTED PSEUDO-SHIFTS ON BANACH SEQUENCE SPACES[J]. Acta mathematica scientia, Series B, 2019
, 39(4)
: 1089
-1102
.
DOI: 10.1007/s10473-019-0413-1
[1] Bayart F, Matheron É. Dynamics of Linear Operators. Cambridge:Cambridge University Press, 2009
[2] Bernal-González L, Grosse-Erdmann K G. The Hypercyclicity Criterion for sequences of operators. Studia Math, 2003, 157(1):17-32
[3] Grosse-Erdmann K G, Peris Manguillot A. Linear Chaos. London:Springer, 2011
[4] Bernal-González L. Disjoint hypercyclic operators. Studia Math, 2007, 182(2):113-131
[5] Bès J, Peris A. Disjointness in hypercyclicity. J Math Anal Appl, 2007, 336:297-315
[6] Bès J, Martin Ö, Sanders R. Weighted shifts and disjoint hypercyclicity. J Oper Theory, 2014, 72(1):15-40
[7] Sanders R, Shkarin S. Existence of disjoint weakly mixing operators that fail to satisfy the Disjoint Hypercyclicity Criterion. J Math Anal Appl, 2014, 417(2):834-855
[8] Bès J, Martin Ö. Compositional disjoint hypercyclicity equals disjoint supercyclicity. Houston J Math, 2012, 38(4):1149-1163
[9] Bès J, Martin Ö, Peris A. Disjoint hypercyclic linear fractional composition operators. J Math Anal Appl, 2011, 381(2):843-856
[10] Martin Ö. Disjoint hypercyclic and supercyclic composition operators[D]. Bowling Green State University, 2010
[11] Liang Y X, Zhou Z H. Disjoint supercyclic powers of weighted shifts on weighted sequence spaces. Turk J Math, 2014, 38:1007-1022
[12] Martin Ö, Sanders R. Disjoint supercyclic weighted shifts. Integr Equ Oper Theory, 2016, 85(2):191-220
[13] Han S A, Liang Y X. Disjoint hypercyclic weighted translations generated by aperiodic elements. Collect Math, 2016, 67(3):347-356
[14] Liang Y X, Xia L. Disjoint supercyclic weighted translations generated by aperiodic elements. Collect Math, 2017, 68:265-278
[15] Wang Y, Zhou Z H. Disjoint hypercyclic powers of weighted pseudo-shifts. Bull Malays Math Sci Soc, 2017, 41(2):1-20. https://doi.org/10.1007/s40840-017-0584-7
[16] Bès J, Martin Ö, Peris A, et al. Disjoint mixing operators. J Funct Anal, 2012, 263(5):1283-1322
[17] Salas H. Dual disjoint hypercyclic operators. J Math Anal Appl, 2011, 374(1):106-117
[18] Shkarin S. A short proof of existence of disjoint hypercyclic operators. J Math Anal Appl, 2010, 367(2):713-715
[19] Zhang L, Zhou Z H. Disjointness in supercyclicity on the algebra of Hilbert-Schmidt operators. Indian J Pure Appl Math, 2015, 46(2):219-228
[20] Salas H. The Strong Disjoint Blow-up/Collapse Property. J Funct Spaces Appl, 2013, 6 pages. Article ID:146517
[21] Grosse-Erdmann K G. Hypercyclic and chaotic weighted shifts. Studia Math, 2000, 139(1):47-68
[22] Hazarika M, Arora S C. Hypercyclic operator weighted shifts. Bull Korean Math Soc, 2004, 41(4):589-598
[23] Liang Y X, Zhou Z H. Hereditarily hypercyclicity and supercyclicity of weighted shifts. J Korean Math Soc, 2014, 51(2):363-382
