Work

Recurrence of Composition Operators on Discrete Banach Spaces

Year: 2026

Type: article

Abstract: Let (T,d) be an unbounded and locally finite metric space that contains a distinguished element o. Let L∞(T) denote the discrete Banach space and L0(T) its subspace of functions vanishing at infinity. First, we establish that the recurrence of a composition operator on the L0(T) space is equivalent to its rigidity. We then provide an equivalent characterization for the uniformly rigid and F-recurrence of Cφ. For the L∞(T) space, the recurrence of the operator is equivalent to the periodicity of the function φ. Second, we explore the concept of disjoint topological recurrence associated with multiple composition operators.

Source: Axioms

DOI: 10.3390/axioms15020137

Authors: Li Zhang, Li Zhang, Mingchao Liu, Liang Zhang, Liang Zhang

Institutions: Tianjin University, Nanyang Normal University

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funders: National Natural Science Foundation of China, Nanyang Normal University, Natural Science Foundation of Henan Province