2024/06/11 by Saak Gabriyelyan, Gabriyelyan, Saak
Computer Science · Mathematics · #46A3 #46E10 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2406.07178
openalex publication_date 2024/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let 1≤ p≤ q≤∞. Being motivated by the classical notions of the Gelfand--Phillips property and the (coarse) Gelfand--Phillips property of order p of Banach spaces, we introduce and study different types of the Gelfand--Phillips property of order (p,q) (the GP(p,q) property) and the coarse Gelfand--Phillips property of order p in the realm of all locally convex spaces. We compare these classes and show that they are stable under taking direct product, direct sums and closed subspaces. It is shown that any locally convex space is a quotient space of a locally convex space with the GP(p,q) property. Characterizations of locally convex spaces with the introduced Gelfand--Phillips type properties are given.