Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

Common Locally Hypercyclic Vectors for a Family of ‎Operators

Document Type : Original Paper

Authors
1 ‎Department of Mathematics‎, ‎College of Sciences‎, ‎Yasouj University‎, ‎Yasouj‎, ‎Iran
2 Department of Mathematics, College of Sciences, Yasouj University, Yasouj, Iran
Abstract
In this research, two main topics in operator theory are investigated. First, we compare topologically transitive operators and locally topologically transitive operators on an arbitrary Banach space \(X\). Next, we introduce common locally hypercyclic vectors for a family of locally topologically transitive operators. Furthermore, we present several structural differences between the ‎set‎ of common locally hypercyclic vectors and the set of common hypercyclic vectors. Indeed, by examining various examples, we demonstrate that the set of common locally hypercyclic vectors may, in some cases, be empty; in others, dense; and in yet others, even non-separable. These cases highlight the distinct behavior of the ‎set‎ of common locally hypercyclic vectors compared to the set of common hypercyclic vectors in operator theory.
Keywords
Subjects

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  • Receive Date 15 May 2025
  • Revise Date 18 August 2025
  • Accept Date 23 December 2025