ꞔ-CYCLICITY FOR CERTAIN CLASSES OF OPERATORS IN BANACH SPACES

Abstract

In this paper, we present new theoretical results concerning ꞔ-cyclicity for certain classical linear operators. Specifically, we characterize all bilateral weighted shift operatorsthat exhibit ꞔ-cyclic behavior and establish a framework that differentiates ꞔ-cyclicity from other forms such as supercyclicity, hypercyclicity, and diskcyclicity. Moreover, we demonstrate that some classical operators, including the composition and multiplication operatorson the Hardy space, fail to be ꞔ-cyclic under general conditions. These findings not only generalize existing criteria but also enrich the understanding of operator dynamics within function spaces.