Weakly and weak^∗ p-convergent operators

2024/05/19 by Saak Gabriyelyan, Gabriyelyan, Saak
Computer Science · Mathematics · #46A3 #46E10 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2405.11518

openalex publication_date 2024/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p∈[1,∞]. Being motivated by weakly p-convergent and weak^∗ p-convergent operators between Banach spaces introduced by Fourie and Zeekoei, we introduce and study the classes of weakly p-convergent and weak^∗ p-convergent operators between arbitrary locally convex spaces. Relationships between these classes of operators are given, and we show that they have ideal properties. Numerous characterizations of weakly p-convergent and weak^∗ p-convergent operators are given.

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