Orbits of the backward shifts with limit points
We show that the bilateral backward shift on ℓp(Z,ω) that has a projective orbit with a non-zero limit point is supercyclic. This phenomenon holds also for Γ-supercyclicity, which extends a result obtained for the first time by Chan and Seceleanu. Moreover, we show that if K is a compact subset of ℓ...
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| Published in: | Journal of mathematical analysis and applications Vol. 537; no. 2; p. 128293 |
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| Abstract | We show that the bilateral backward shift on ℓp(Z,ω) that has a projective orbit with a non-zero limit point is supercyclic. This phenomenon holds also for Γ-supercyclicity, which extends a result obtained for the first time by Chan and Seceleanu. Moreover, we show that if K is a compact subset of ℓp(N,ω) such that its orbit under the unilateral backward shift B on ℓp(N,ω) has a non-zero weak limit point, then B is hypercyclic. Similar results for translation semigroups on weighted Lebesgue spaces are obtained. |
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| AbstractList | We show that the bilateral backward shift on ℓp(Z,ω) that has a projective orbit with a non-zero limit point is supercyclic. This phenomenon holds also for Γ-supercyclicity, which extends a result obtained for the first time by Chan and Seceleanu. Moreover, we show that if K is a compact subset of ℓp(N,ω) such that its orbit under the unilateral backward shift B on ℓp(N,ω) has a non-zero weak limit point, then B is hypercyclic. Similar results for translation semigroups on weighted Lebesgue spaces are obtained. |
| ArticleNumber | 128293 |
| Author | Abakumov, Evgeny Abbar, Arafat |
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| Cites_doi | 10.1090/S0002-9947-1995-1249890-6 10.4064/sm-135-1-55-74 10.1090/S0273-0979-99-00788-0 10.4064/sm-32-1-17-22 10.1016/j.jmaa.2017.11.046 10.1007/s11785-019-00941-y 10.1016/j.jmaa.2010.08.033 10.1307/mmj/1029005229 10.1142/S0218127418500761 10.1007/s11785-013-0348-9 10.1090/S0002-9939-03-06960-0 10.1016/j.jmaa.2020.124709 10.1017/S0143385797084976 10.1007/s00020-013-2100-2 10.1016/j.jfa.2006.12.008 10.7146/math.scand.a-15207 10.1016/j.jfa.2016.03.005 |
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| Keywords | Backward shift Recurrence Supercyclicity Hypercyclicity Translation semigroup Orbital limit points |
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| References | Charpentier, Ernst, Menet (br0080) 2016; 270 Grosse-Erdmann, Peris (br0170) 2011 Abbar (br0040) 2020 He, Huang, Yin (br0180) 2018; 28 Abbar (br0020) 2019; 13 Costakis, Manoussos, Parissis (br0100) 2014; 8 Rolewicz (br0200) 1969; 32 Desch, Schappacher, Webb (br0140) 1997; 17 Salas (br0220) 1999; 135 Yin, Wei (br0240) 2018; 460 Salas (br0210) 1995; 347 Bonilla, Grosse-Erdmann (br0070) 2020 Abbar (br0030) 2019; 129 Chan, Seceleanu (br0130) 2014; 78 Matsui, Yamada, Takeo (br0190) 2003; 131 Abakumov (br0010) 1995; 42 Chan, Seceleanu (br0120) 2012; 67 Conejero, Müller, Peris (br0090) 2007; 244 Costakis, Parissis (br0110) 2012; 110 Feldman (br0150) 2003; 50 Bayart, Matheron (br0060) 2009; vol. 179 Abbar, Kuznetsova (br0050) 2021; 495 Grosse-Erdmann (br0160) 1999; 36 Shkarin (br0230) 2011; 382 Chan (10.1016/j.jmaa.2024.128293_br0120) 2012; 67 Abbar (10.1016/j.jmaa.2024.128293_br0040) 2020 Rolewicz (10.1016/j.jmaa.2024.128293_br0200) 1969; 32 Salas (10.1016/j.jmaa.2024.128293_br0220) 1999; 135 Shkarin (10.1016/j.jmaa.2024.128293_br0230) 2011; 382 Desch (10.1016/j.jmaa.2024.128293_br0140) 1997; 17 Feldman (10.1016/j.jmaa.2024.128293_br0150) 2003; 50 Grosse-Erdmann (10.1016/j.jmaa.2024.128293_br0160) 1999; 36 Abbar (10.1016/j.jmaa.2024.128293_br0020) 2019; 13 Abbar (10.1016/j.jmaa.2024.128293_br0050) 2021; 495 Matsui (10.1016/j.jmaa.2024.128293_br0190) 2003; 131 Conejero (10.1016/j.jmaa.2024.128293_br0090) 2007; 244 Costakis (10.1016/j.jmaa.2024.128293_br0100) 2014; 8 Abbar (10.1016/j.jmaa.2024.128293_br0030) 2019; 129 He (10.1016/j.jmaa.2024.128293_br0180) 2018; 28 Yin (10.1016/j.jmaa.2024.128293_br0240) 2018; 460 Salas (10.1016/j.jmaa.2024.128293_br0210) 1995; 347 Grosse-Erdmann (10.1016/j.jmaa.2024.128293_br0170) 2011 Bonilla (10.1016/j.jmaa.2024.128293_br0070) Abakumov (10.1016/j.jmaa.2024.128293_br0010) 1995; 42 Charpentier (10.1016/j.jmaa.2024.128293_br0080) 2016; 270 Costakis (10.1016/j.jmaa.2024.128293_br0110) 2012; 110 Chan (10.1016/j.jmaa.2024.128293_br0130) 2014; 78 Bayart (10.1016/j.jmaa.2024.128293_br0060) 2009; vol. 179 |
| References_xml | – volume: 13 start-page: 3923 year: 2019 end-page: 3942 ident: br0020 article-title: Γ-supercyclicity for strongly continuous semigroups publication-title: Complex Anal. Oper. Theory – year: 2020 ident: br0040 article-title: Dynamique linéaire: ensembles hypercycliques, semigroupes d'opérateurs, translations sur les groupes – year: 2011 ident: br0170 article-title: Linear Chaos – volume: 131 start-page: 3535 year: 2003 end-page: 3546 ident: br0190 article-title: Supercyclic and chaotic translation semigroups publication-title: Proc. Am. Math. Soc. – volume: 244 start-page: 342 year: 2007 end-page: 348 ident: br0090 article-title: Hypercyclic behaviour of operators in a hypercyclic publication-title: J. Funct. Anal. – volume: 28 year: 2018 ident: br0180 article-title: -class weighted backward shifts publication-title: Int. J. Bifurc. Chaos – volume: 135 start-page: 55 year: 1999 end-page: 74 ident: br0220 article-title: Supercyclicity and weighted shifts publication-title: Stud. Math. – volume: 17 start-page: 793 year: 1997 end-page: 819 ident: br0140 article-title: Hypercyclic and chaotic semigroups of linear operators publication-title: Ergod. Theory Dyn. Syst. – volume: 50 start-page: 107 year: 2003 end-page: 117 ident: br0150 article-title: Countably hypercyclic operators publication-title: J. Oper. Theory – volume: 8 start-page: 1601 year: 2014 end-page: 1643 ident: br0100 article-title: Recurrent linear operators publication-title: Complex Anal. Oper. Theory – volume: 42 start-page: 277 year: 1995 end-page: 299 ident: br0010 article-title: Cyclicity and approximation by lacunary power series publication-title: Mich. Math. J. – volume: 270 start-page: 4443 year: 2016 end-page: 4465 ident: br0080 article-title: Γ-supercyclicity publication-title: J. Funct. Anal. – volume: 78 start-page: 225 year: 2014 end-page: 232 ident: br0130 article-title: Cyclicity of vectors with orbital limit points for backward shifts publication-title: Integral Equ. Oper. Theory – volume: 382 start-page: 516 year: 2011 end-page: 522 ident: br0230 article-title: On supercyclicity of operators from a supercyclic semigroup publication-title: J. Math. Anal. Appl. – volume: 110 start-page: 251 year: 2012 end-page: 272 ident: br0110 article-title: Szemerédi's theorem, frequent hypercyclicity and multiple recurrence publication-title: Math. Scand. – volume: 67 start-page: 257 year: 2012 end-page: 277 ident: br0120 article-title: Hypercyclicity of shifts as a zero-one law of orbital limit points publication-title: J. Oper. Theory – volume: 32 start-page: 17 year: 1969 end-page: 22 ident: br0200 article-title: On orbits of elements publication-title: Stud. Math. – volume: 347 start-page: 993 year: 1995 end-page: 1004 ident: br0210 article-title: Hypercyclic weighted shifts publication-title: Trans. Am. Math. Soc. – volume: 460 start-page: 203 year: 2018 end-page: 215 ident: br0240 article-title: Recurrence and topological entropy of translation operators publication-title: J. Math. Anal. Appl. – volume: 36 start-page: 345 year: 1999 end-page: 381 ident: br0160 article-title: Universal families and hypercyclic operators publication-title: Bull. Am. Math. Soc. – volume: 495 year: 2021 ident: br0050 article-title: Γ-supercyclicity of families of translates in weighted publication-title: J. Math. Anal. Appl. – year: 2020 ident: br0070 article-title: Zero-one law of orbital limit points for weighted shifts – volume: 129 start-page: 73 year: 2019 end-page: 79 ident: br0030 article-title: Γ-supercyclicity for bilateral shift operators and translation semigroups publication-title: Bul. L.N. Gumilyov ENU. Math. Comput. Sci. Mech. Ser. – volume: vol. 179 year: 2009 ident: br0060 article-title: Dynamics of Linear Operators publication-title: Cambridge Tracts in Mathematics – year: 2011 ident: 10.1016/j.jmaa.2024.128293_br0170 – volume: 129 start-page: 73 issue: 4 year: 2019 ident: 10.1016/j.jmaa.2024.128293_br0030 article-title: Γ-supercyclicity for bilateral shift operators and translation semigroups publication-title: Bul. L.N. Gumilyov ENU. Math. Comput. Sci. Mech. Ser. – year: 2020 ident: 10.1016/j.jmaa.2024.128293_br0040 – volume: 347 start-page: 993 issue: 3 year: 1995 ident: 10.1016/j.jmaa.2024.128293_br0210 article-title: Hypercyclic weighted shifts publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1995-1249890-6 – volume: 135 start-page: 55 issue: 1 year: 1999 ident: 10.1016/j.jmaa.2024.128293_br0220 article-title: Supercyclicity and weighted shifts publication-title: Stud. Math. doi: 10.4064/sm-135-1-55-74 – volume: 36 start-page: 345 issue: 3 year: 1999 ident: 10.1016/j.jmaa.2024.128293_br0160 article-title: Universal families and hypercyclic operators publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0273-0979-99-00788-0 – volume: 32 start-page: 17 issue: 1 year: 1969 ident: 10.1016/j.jmaa.2024.128293_br0200 article-title: On orbits of elements publication-title: Stud. Math. doi: 10.4064/sm-32-1-17-22 – volume: 460 start-page: 203 issue: 1 year: 2018 ident: 10.1016/j.jmaa.2024.128293_br0240 article-title: Recurrence and topological entropy of translation operators publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2017.11.046 – volume: 13 start-page: 3923 issue: 8 year: 2019 ident: 10.1016/j.jmaa.2024.128293_br0020 article-title: Γ-supercyclicity for strongly continuous semigroups publication-title: Complex Anal. Oper. Theory doi: 10.1007/s11785-019-00941-y – volume: 382 start-page: 516 issue: 2 year: 2011 ident: 10.1016/j.jmaa.2024.128293_br0230 article-title: On supercyclicity of operators from a supercyclic semigroup publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2010.08.033 – volume: 42 start-page: 277 issue: 2 year: 1995 ident: 10.1016/j.jmaa.2024.128293_br0010 article-title: Cyclicity and approximation by lacunary power series publication-title: Mich. Math. J. doi: 10.1307/mmj/1029005229 – ident: 10.1016/j.jmaa.2024.128293_br0070 – volume: 28 issue: 06 year: 2018 ident: 10.1016/j.jmaa.2024.128293_br0180 article-title: JF-class weighted backward shifts publication-title: Int. J. Bifurc. Chaos doi: 10.1142/S0218127418500761 – volume: 8 start-page: 1601 issue: 8 year: 2014 ident: 10.1016/j.jmaa.2024.128293_br0100 article-title: Recurrent linear operators publication-title: Complex Anal. Oper. Theory doi: 10.1007/s11785-013-0348-9 – volume: 131 start-page: 3535 issue: 11 year: 2003 ident: 10.1016/j.jmaa.2024.128293_br0190 article-title: Supercyclic and chaotic translation semigroups publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-03-06960-0 – volume: 495 issue: 1 year: 2021 ident: 10.1016/j.jmaa.2024.128293_br0050 article-title: Γ-supercyclicity of families of translates in weighted Lp-spaces on locally compact groups publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2020.124709 – volume: 17 start-page: 793 issue: 4 year: 1997 ident: 10.1016/j.jmaa.2024.128293_br0140 article-title: Hypercyclic and chaotic semigroups of linear operators publication-title: Ergod. Theory Dyn. Syst. doi: 10.1017/S0143385797084976 – volume: 50 start-page: 107 issue: 1 year: 2003 ident: 10.1016/j.jmaa.2024.128293_br0150 article-title: Countably hypercyclic operators publication-title: J. Oper. Theory – volume: 78 start-page: 225 issue: 2 year: 2014 ident: 10.1016/j.jmaa.2024.128293_br0130 article-title: Cyclicity of vectors with orbital limit points for backward shifts publication-title: Integral Equ. Oper. Theory doi: 10.1007/s00020-013-2100-2 – volume: 244 start-page: 342 issue: 1 year: 2007 ident: 10.1016/j.jmaa.2024.128293_br0090 article-title: Hypercyclic behaviour of operators in a hypercyclic c0-semigroup publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2006.12.008 – volume: vol. 179 year: 2009 ident: 10.1016/j.jmaa.2024.128293_br0060 article-title: Dynamics of Linear Operators – volume: 67 start-page: 257 issue: 1 year: 2012 ident: 10.1016/j.jmaa.2024.128293_br0120 article-title: Hypercyclicity of shifts as a zero-one law of orbital limit points publication-title: J. Oper. Theory – volume: 110 start-page: 251 issue: 2 year: 2012 ident: 10.1016/j.jmaa.2024.128293_br0110 article-title: Szemerédi's theorem, frequent hypercyclicity and multiple recurrence publication-title: Math. Scand. doi: 10.7146/math.scand.a-15207 – volume: 270 start-page: 4443 issue: 12 year: 2016 ident: 10.1016/j.jmaa.2024.128293_br0080 article-title: Γ-supercyclicity publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2016.03.005 |
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| Snippet | We show that the bilateral backward shift on ℓp(Z,ω) that has a projective orbit with a non-zero limit point is supercyclic. This phenomenon holds also for... |
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| SubjectTerms | Backward shift Hypercyclicity Orbital limit points Recurrence Supercyclicity Translation semigroup |
| Title | Orbits of the backward shifts with limit points |
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