Dynamics of linear operators on non-Archimedean vector spaces

被引:5
|
作者
Mukhamedov, Farrukh [1 ]
Khakimov, Otabek [2 ]
机构
[1] United Arab Emirates Univ, Dept Math Sci, Coll Sci, POB 15551, Abu Dhabi, U Arab Emirates
[2] Acad Sci Uzbek, Inst Math, 29 Dormon Yoli Str, Tashkent 100125, Uzbekistan
关键词
non-Archimedean valuation; hypercylic operator; supercyclic operator; backward shift operator; INVARIANT; SHIFT;
D O I
10.36045/bbms/1523412055
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In the present paper we study dynamics of linear operators defined on topological vector space over non-Archimedean valued fields. We give sufficient and necessary conditions of hypercyclicity (resp. supercyclicity) of linear operators on separable F-spaces. It is proven that a linear operator T on topological vector space X is hypercyclic (supercyclic) if it satisfies Hypercyclicity (resp. Supercyclicity) Criterion. We consider backward shifts on c(0)(Z) and c(0)(N), respectively, and characterize hypercyclicity and supercyclicity of such kinds of shifts. Finally, we study hypercyclicity, supercyclicity of operators lambda I + mu B, where I is identity and B is backward shift. We note that there are essential differences between the non-Archimedean and real cases.
引用
收藏
页码:85 / 105
页数:21
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