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Some properties of subspace convex-cyclic operators

Dilan Ahmed1,2, Mudhafar F. Hama3, Jarosław Wožniak4 and Karwan Jwamer3


1 Mathematics Department, College of Education, University of Sulaimani,  Sulaimani, Kurditan Region – Iraq

2Computer Engineering-College of Engineering, Komar University of Science and Technology, Sulaimani , Kurditan Region –  Iraq.

3 Mathematics Department,College of Science University of Sulaimani,  Sulaimani, Kurditan Region – Iraq

4 Institute of Mathematics, Department of Mathematics and Physics, University of Szczecin, Ul. Wielkopolska 15, 70-451 Szczecin, Poland   

Original: 20 July 2019       Revised: 10 January 2020     Accepted:April 2020        Published online: 20 June 2020  

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On a Banach space X, a bounded linear operator A is a called subspace convex-cyclic associated with W as a subspace, if the set  is dense in W for a vector . In this work, we use Hahn- Banach Theorem to show that the extending linear functional preserve subspace convex-cyclic operator property. Also, the algebraic structures of subspace convex-cyclic vectors can be determined, such as the spectrum.

Key Words: convex-cyclic operator; Hahn-Banach theorem; convex-cyclic spectral.


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