Some properties of subspace convex-cyclic operators

Authors

  • Dilan Ahmed Mathematics Department, College of Education, University of Sulaimani, Kurditan Region, Iraq. & Computer Engineering, College of Engineering, Komar University of Science and Technology, Sulaimani, Kurdistan Region, Iraq. Author
  • Mudhafar F. Hama Mathematics Department, College of Science, University of Sulaimani, Kurdistan Region, Iraq. Author
  • Jarosław Wožniak Institute of Mathematics, Department of Mathematics and Physics, University of Szczecin, Ul. Wielkopolska 15, 70-451 Szczecin, Poland. Author
  • Karwan Jwamer Mathematics Department, College of Science, University of Sulaimani, Kurdistan Region, Iraq. Author

DOI:

https://doi.org/10.17656/jzs.10797

Keywords:

Convex-cyclic operator, Hahn-Banach theorem, Convex-cyclic spectral

Abstract

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.

References

D. Ahmed, M. Hama, J. Wozniak and K. Jwamer, "On subspace convex-cyclic operators", arXiv:1905.04781 [math.DS].

Sh. Axler, "Linear Algebra Done Right", Springer International Publishing, Edu 3, (2015). DOI:10.1007/978-3-319-11080-6. DOI: https://doi.org/10.1007/978-3-319-11080-6

F. Bayart, E. Matheron, "Dynamics of Linear Operators", Cambridge University Press, New York, (2009). DOI: https://doi.org/10.1017/CBO9780511581113

T. Bermudez, A. Bonilla and N. Feldman, "on convex-cyclic operator", J. Math. Anal and Appl. Vol. 434, No. 2, pp.1166-1181. (2016). DOI: https://doi.org/10.1016/j.jmaa.2015.09.053

V.I. Bogachev and O.G. Smolyanov, "Topological Vector Spaces and Their Applications", Springer International Publishing, Edu 1, (2017). DOI: https://doi.org/10.1007/978-3-319-57117-1_1

P. S. Bourdon, N. S. Feldman, "Somewhere dense orbits are everywhere dense", Indiana Univ. Math. J. Vol. 52, No. 3, pp. 811-819. (2003). DOI: https://doi.org/10.1512/iumj.2003.52.2303

K. G. Grosse-Erdmann, A. Peris, "Linear Chaos", Universitext, Springer, (2011). DOI: https://doi.org/10.1007/978-1-4471-2170-1

R. R. Jiménez-Munguía, R. A. Martínez-Avendaño and A. Peris, "Some questions about subspace-hypercyclic operators", Journal of Mathematical Analysis and Applications. Vol. 408, No. 1, pp. 209-212. (2013). DOI: https://doi.org/10.1016/j.jmaa.2013.05.068

C. M. Le, "On subspace-hypercyclic operators", Amer. Math. Soc. Vol. 139, No. 8, pp. 2847–2852. (2011). DOI: https://doi.org/10.1090/S0002-9939-2011-10754-8

B. F. Madore, R. A. Martínez-Avendaño, "Subspace hypercyclicity", J. Math. Anal. Appl. Vol. 373, No. 2, pp. 502-511. (2011). DOI: https://doi.org/10.1016/j.jmaa.2010.07.049

H. Rezaei, "On the convex hull generated by orbit of operators", Linear Algebra and its Applications. Vol. 438, No. 11, pp. 4190-4203. (2013). DOI: https://doi.org/10.1016/j.laa.2013.02.002

H. Rezaei, "Notes on subspace-hypercyclic operators", Journal of Mathematical Analysis and Applications. Vol. 397, No. 1, pp. 428-433. (2013). DOI: https://doi.org/10.1016/j.jmaa.2012.08.002

W. Rudin, "Functional analysis", McGraw-Hill Series in Higher Mathematics, Mc-Graw Hill, Edu 1, (1973).

Published

2020-06-20

How to Cite

Some properties of subspace convex-cyclic operators. (2020). Journal of Zankoy Sulaimani - Part A, 22(1), 345-352. https://doi.org/10.17656/jzs.10797