Disjoint codiskcyclic operators

El Mostafa  Sadouk; Otmane Benchiheb; Mohamed  Amouch

doi:10.5269/bspm.75978

El Mostafa Sadouk
Otmane Benchiheb Université Chouaïb Doukkali – Faculté des Sciences d'El Jadida
Mohamed Amouch

Abstract

This article introduces and examines the concept of disjoint codiskcyclicity for a finite number of operators acting on an infinite-dimensional separable Banach space, providing a corresponding criterion. Furthermore, it characterizes the disjoint codiskcyclicity of finitely many distinct powers of weighted shifts in both unilateral and bilateral cases on a sequence space.

Downloads

Download data is not yet available.

References

Amouch, M., Bachir, A., Benchiheb, O., Mecheri, S. (2023). Weakly recurrent operators. Mediterranean Journal of Mathematics, 20(3), 169.

Amouch, M., Benchiheb, O. (2020). Diskcyclicity of sets of operators and applications. Acta Mathematica Sinica, English Series, 36, 1203–1220.

Amouch, M., Benchiheb, O. (2022). Codiskcyclic sets of operators on complex topological vector spaces. Proyecciones Journal of Mathematics, 41(6), 1439–1456.

Bayart, F., Matheron, E. (2009). Dynamics of linear operators. Cambridge University Press.

Benchiheb, O., Amouch, M. (2024). On recurrent sets of operators. Boletim da Sociedade Paranaense de Matematica, 42, 1–9.

Benchiheb, O., Amouch, M. (2024). Subspace-super recurrence of operators. Filomat, 38(9), 3093–3103.

Benchiheb, O., Sadek, F., Amouch, M. (2023). On super-rigid and uniformly super-rigid operators. Afrika Matematika, 34(1), 6.

Bernal-Gonzalez, L. (2007). Disjoint hypercyclic operators. Studia Mathematica, 2, 113–131.

Bes, J., Peris, A. (2007). Disjointness in hypercyclicity. Journal of Mathematical Analysis and Applications, 336, 297–315.

Godefroy, G., Shapiro, J.H. (1991). Operators with dense, invariant, cyclic vector manifolds. Journal of Functional Analysis, 98, 229–269.

Hilden, H.M., Wallen, L.J. (1994). Some cyclic and non-cyclic vectors of certain operators. Indiana University Mathematics Journal, 23, 557–565.

Jamil, Z.Z. (2002). Cyclic phenomena of operators on Hilbert space. Thesis, University of Baghdad.

Karim, N., Benchiheb, O., Amouch, M. (2024). Faber-hypercyclic semigroups of linear operators. Filomat, 38(25), 8869–8876.

Karim, N., Benchiheb, O., Amouch, M. (2024). Disjoint strong transitivity of composition operators. Collectanea Mathematica, 75(1), 171–187.

Leon-Saavedra, F., Montes-Rodrıguez, A. (1997). Linear structure of hypercyclic vectors. Journal of Functional Analysis, 148, 524–545.

Liang, Y.X., Zhou, Z.H. (2014). Disjoint supercyclic powers of weighted shifts on weighted sequence spaces. Turkish Journal of Mathematics, 38, 1007–1022.

Liang, Y.X., Zhou, Z.H. (2018). Disjoint supercyclic weighted composition operators. Bulletin of the Korean Mathematical Society, 55(4), 1137–1147.

Martin, O. (2011). Disjoint hypercyclic and supercyclic composition operators. PhD thesis, Bowling Green State University.

Martin, O., Sanders, R. (2016). Disjoint supercyclic weighted shifts. Integral Equations and Operator Theory, 85, 191–220.

Rolewicz, S. (1969). On orbits of elements. Studia Mathematica, 32, 17–22.

Sadouk, E.M., Benchiheb, O., Amouch, M. (2024). Disjoint topologically super-recurrent operators. Filomat, 38(30), 10495–10504.

Sadouk, E.M., Benchiheb, O., Amouch, M. (2024). C-Recurrent operators. Palestine Journal of Mathematics, 13(4).

Salas, H. (1995). Hypercyclic weighted shifts. Transactions of the American Mathematical Society, 347(3), 993–1004.

Salas, H. (1999). Supercyclicity and weighted shifts. Studia Mathematica, 135(1), 55–74.

Wang, C., Zhou, Z.H., Zhang, L. (2022). Disjoint diskcyclicity of weighted shifts. Open Mathematics, 20, 820–828.

Wang, Y., Zhou, H.G. (2018). Disk-cyclic and codisk-cyclic weighted pseudo-shifts. Bulletin of the Belgian Mathematical Society - Simon Stevin, 25(2), 209–224.