Subring structures in C(X) defined by absolute values
Abstract
In this paper, we introduce and study two new classes of subrings of C(X): norm-closed subrings and norm-reflecting subrings. A subring ℝ ⊆ S ⊆ C ( X ) is said to be norm-closed if for every f ∈ S , the function |f| ∈ S; it is norm-reflecting if |f| ∈ S implies f ∈ S. These concepts are inspired by the lattice structure of C(X), particularly the operation of taking absolute values. We provide characterizations of norm-closed (norm-reflecting) subrings. Several examples and counterexamples are presented to illustrate the distinctions and connections between these classes.
Fields of Study & Subjects
Advanced Banach Space Theory
Advanced Operator Algebra Research
Holomorphic and Operator Theory
Publication details
- Journal / source
- Applied General Topology
- Volume
- 27
- Issue
- 1
- Pages
- 24082–24082
- Publication date
- 5 February 2026
- Language
- EN