DISJOINT SUPERCYCLIC WEIGHTED PSEUDO-SHIFTS ON BANACH SEQUENCE SPACES

doi:10.1007/s10473-019-0413-1

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (4): 1089-1102.doi: 10.1007/s10473-019-0413-1

DISJOINT SUPERCYCLIC WEIGHTED PSEUDO-SHIFTS ON BANACH SEQUENCE SPACES

王亚¹, 梁玉霞²

1. Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, China;
2. School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China

收稿日期:2018-01-19 出版日期:2019-08-25 发布日期:2019-09-12
作者简介:Ya WANG,E-mail:wangyasjxsy0802@163.com;Yu-Xia LIANG,E-mail:liangyx1986@126.com
基金资助:
This work is supported by the Research Project of Tianjin Municipal Education Commission (2017KJ124).

DISJOINT SUPERCYCLIC WEIGHTED PSEUDO-SHIFTS ON BANACH SEQUENCE SPACES

Ya WANG¹, Yu-Xia LIANG²

1. Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, China;
2. School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China

Received:2018-01-19 Online:2019-08-25 Published:2019-09-12
Supported by:
This work is supported by the Research Project of Tianjin Municipal Education Commission (2017KJ124).

摘要/Abstract

摘要： 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.

关键词: Disjoint supercyclicity, weighted pseudo-shifts, disjoint Blow-up/collapse Property

Abstract: 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.

Key words: Disjoint supercyclicity, weighted pseudo-shifts, disjoint Blow-up/collapse Property

中图分类号:

47A16

王亚, 梁玉霞. DISJOINT SUPERCYCLIC WEIGHTED PSEUDO-SHIFTS ON BANACH SEQUENCE SPACES[J]. 数学物理学报(英文版), 2019, 39(4): 1089-1102.

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.

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DISJOINT SUPERCYCLIC WEIGHTED PSEUDO-SHIFTS ON BANACH SEQUENCE SPACES

DISJOINT SUPERCYCLIC WEIGHTED PSEUDO-SHIFTS ON BANACH SEQUENCE SPACES

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