Frequent, disjoint hypercyclicity and strong topological transitivity of generalized weighted shift operators on Hilbert C-modules

Q: What type of study is this?

This is a Quantitative Study study.

Song-Ung Ri; Hyonhui Ju; Jin‐Myong Kim

doi:10.48550/arxiv.2510.00445

October 1, 2025Open Access

Frequent, disjoint hypercyclicity and strong topological transitivity of generalized weighted shift operators on Hilbert C-modules

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Key Points

Frequent hypercyclicity can be achieved using generalized weighted shift operators in specific conditions.
The study reveals how chaos and disjoint hypercyclicity exhibit strong topological transitivity in the analyzed systems.
F-transitivity is a key property for understanding the dynamics on Hilbert C-modules, with implications for operator theory.
The findings expand the understanding of dynamical systems through the lens of algebraic structures in Hilbert spaces.

Implication

This analysis shows frequent hypercyclicity and chaos in weighted shift operators, indicating new insights into their dynamics.

Abstract

In this paper we study some dynamical properties such as Frequent Hypercyclicity Criterion, chaos, disjoint hypercyclicity and F-transitivity via Furstenberg family F for generalized bilateral weighted shift operator on the standard Hilbert C-module over C-algebra of compact operators on a separable Hilbert space.

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Cite This Study

Ri et al. (2025) studied this question.

synapsesocial.com/papers/68e24e6fd6d66a53c2473f51 https://doi.org/10.48550/arxiv.2510.00445

View Full Paper

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Frequent, disjoint hypercyclicity and strong topological transitivity of generalized weighted shift operators on Hilbert C-modules

Key Points

Implication

Abstract

Discussion

Cite This Study

Frequent, disjoint hypercyclicity and strong topological transitivity of generalized weighted shift operators on Hilbert C-modules

Key Points

Implication

Abstract

Discussion

Cite This Study

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