On stability of restricted center properties and continuity of restricted center map under ℓ_p-direct sum

2025/10/02 by Pananghat Gayathri, P, Gayathri, Vamsinadh Thota +1
Computer Science · Mathematics · #41A65 #46B20 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2510.01955

openalex publication_date 2025/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the stability of various restricted center properties and certain continuity properties of the restricted center map. We observe that restricted center property, property-(P₁) and semi-continuity properties of the restricted center map are preserved under ℓ_p-direct sum (1 ≤ p < ∞). It is shown that property-(P₂) is stable under finite ℓ_p-direct sum, but not under infinite ℓ_p-direct sum. Additionally, we introduce a notion called property-(lP₂) as a sufficient condition for the continuity of the restricted center map. Further, the stability of property-(lP₂) is established.

Related

• On property-(P₁) and semi-continuity properties of restricted Chebyshev-center maps in ℓ_∞-direct sums
• Some stability properties of restricted Chebyshev centers in Banach spaces
• Restricted Chebyshev centers in L₁-predual spaces
• Non-existence of greedy bases in direct sums of mixed ℓ_p spaces
• Sets of Salem type and sharpness of the L²-Fourier restriction theorem