On various classes of hypercyclic and topologically transitive operators on Banach spaces

Hypercyclicity and topological transitivity are the main concepts in topological dynamics of operators. In this talk, we shall present characterizations of several classes of topologically transitive operators, such as weighted compositions on certain function spaces, left multipliers on Schatten $p$-ideals, generalized weighted shifts on Hilbert $C^*$-modules, the adjoint of weighted composition operators on the space of Radon measures etc… Also, we shall provide concrete examples.
The talk will be based on the following papers.

• Ivković, S., Tabatabaie, S.M. Disjoint Linear Dynamical Properties of Elementary Operators. Bull. Iran. Math. Soc. 49, 63 (2023). https://doi.org/10.1007/s41980-023-00808-1
  
• Ivković, S., Tabatabaie, S.M. Hypercyclic Generalized Shift Operators. Complex Anal. Oper. Theory 17, 60 (2023). https://doi.org/10.1007/s11785-023-01376-2
  
• Ivković, S., Tabatabaie, S.M. Hypercyclic Translation Operators on the Algebra of Compact Operators. Iran J Sci Technol Trans Sci 45, 1765–1775 (2021). https://doi.org/10.1007/s40995-021-01186-1
  
• Ivković, S. Hypercyclic operators on Hilbert $C^*$-modules, FILOMAT vol. 38 no. 6 (2024), 1901–1913 https://doi.org/10.2298/FIL2406901I6
  
• Ivković, S. Dynamics of operators on the space of Radon measures, to appear in Analysis, Approximation, Optimization: Computation and Applications - In Honor of Gradimir V. Milovanović on the Occasion of his 75th Anniversary (edited by: M. Stanić, M. Albijanić, D. Djurčić, M. Spalević), Springer Optimization and its Applications https://doi.org/10.48550/arXiv.2310.10868