Cyclic Dynamics of Operator Tuples Under Semigroup Actions on Banach Spaces

Nareen Bamerni

doi:10.65463/jprm.2026243.

Authors

Nareen Bamerni Department of Mathematics, University of Duhok, Kurdistan Region, Iraq.

DOI:

https://doi.org/10.65463/jprm.2026243.

Keywords:

G-cyclic operators, tuples of operators

Abstract

This article investigates the concept of G-cyclicity for tuples of commuting bounded linear operators on separable infinite-dimensional Banach spaces. We characterize G-cyclic tuples and introduce the related notion of G-transitivity. Furthermore, we establish sufficient conditions—called the G-cyclic tuple criterion—under which a tuple becomes G-cyclic. These results extend the classical theory of hypercyclic and supercyclic operators to a broader semigroup setting. Illustrative examples, structural results, and applications to quotient and direct sum operators are also provided.

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