Year: 2026
Type: article
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.
Source: Applied General Topology
DOI: 10.4995/agt.24082
Author: Mohammad Ali Siavoshi
Institution: Shahid Chamran University of Ahvaz
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Award: G7043500658
OpenAlex ID: W7127990238