Codiskcyclic sets of operators on complex topological vector spaces

• Amouch, Mohamed ; Benchiheb, Otmane ^[1]
  1. [1] Chouaib Doukkali University.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 6, 2022, págs. 1439-1456
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-5011
• Enlaces
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• Resumen

  • Let X be a complex topological vector space and L(X) the set of all continuous linear operators on X. In this paper, we extend the notion of the codiskcyclicity of a single operator T ∈ L(X) to a set of operators Γ ⊂ L(X). We prove some results for codiskcyclic sets of operators and we establish a codiskcyclicity criterion. As an application, we study the codiskcyclicity of C0-semigroups of operators.

• Referencias bibliográficas
  • M. Amouch and O. Benchiheb, ”Some versions of supercyclicity of a s set of operators”, Filomat, vol. 35, no. 5, pp. 1619-1627, 2021. https://doi.org/10.2298/fil2105619a
  • M. Amouch and O. Benchiheb, ”Diskcyclicity of sets of operators and applications”, Acta Mathematica Sinica, English Series, vol. 36, no. 11,...
  • M. Amouch and O. Benchiheb, ”On cyclic sets of operators”, Rendiconti del Circolo Matematico di Palermo Series 2, vol. 68, no. 3, pp. 521-529,...
  • M. Amouch and O. Benchiheb, ”On linear dynamics of sets of operators”, Turkish Journal of Mathematics, vol. 43, no. 1, pp. 402-411, 2019....
  • M. Ansari, K. Hedayatian and B. Khani-robati, ”On the density and transitivity of sets of operators”, Turkish Journal of Mathematics, vol....
  • M. Ansari, K. Hedayatian, B. Khani-robati and A. Moradi, “A note on topological and strict transitivity”, Iranian Journal of Science and Technology,...
  • F. Bayart and E. Matheron, Dynamics of linear operators. New York: Cambridge University Press, 2009.
  • J. B. Conway, A course in Functional Analysis. New York: Springer, 1985.
  • K.-G. Grosse-Erdmann and A. Peris Manguillot, Linear chaos. London: Springer, 2011.
  • K. G. Grosse-Erdmann, “Universal families and hypercyclic operators”, Bulletin of the American Mathematical Society, vol. 36, no. 3, pp. 345-381,...
  • H. M. Hilden and L. J. Wallen, “Some cyclic and non-cyclic vectors of certain operators”, Indiana University Mathematics Journal, vol. 23,...
  • Y. X. Liang and Z. H. Zhou, ”Disk-cyclic and Codisk-cyclic tuples of the adjoint weighted composition operators on Hilbert spaces”, Bulletin...
  • Y. X. Liang and Z. H. Zhou, “Disk-cyclic and Codisk-cyclic of certain shift operators”, Operators and Matrices, vol. 9, no. 4, pp. 831-846,...
  • A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. New York: Springer, 1983.
  • Y. Wang, H. G. Zeng, ”Disk-cyclic and codisk-cyclic weighted pseudo-shifts”, Bulletin of the Belgian Mathematical Society-Simon Stevin, vol....
  • J. Wengenroth, ”Hypercyclic operators on non-locally convex spaces”, Proceedings of the American Mathematical Society, vol. 131, pp. 1759-1761,...
  • J. Woźniak, D. Ahmed, M. Hama, K. Jwamer, ”On Subspace Convex-Cyclic Operators”, Journal of Mathematical Physics, Analysis, Geometry, vol....
  • Z. J. Zeana, “Cyclic phenomena of operators on Hilbert space”, Ph.D. Thesis, University of Baghdad, Iraq, 2002.