Lattice copies and applications for weak L- and M-weakly compact operators on Banach lattices

2019/03/11 by Zhangjun Wang, Wang, Zhangjun, Zili Chen +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1903.04179

openalex publication_date 2019/03/11 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

Several recent papers investigated lattice copies and unbounded convergences in Banach lattices. In this paper, we first solve the problem of RV and LA which is an extension of the well-known James distortion theorem. Using lattice copies and unbounded convergence, then we introduce weak L- and M-weakly compact operators on Banach lattices and research the relationship between these operators and L- and M-weakly compact operators. Finally, we study the compactness of weak L-weakly compact and weak M-weakly compact operators.

Related

• Unbounded M-weakly and unbounded L-weakly compact operators
• Unbounded convergence in Banach lattices and applications
• Some characterizations of L-weakly compact sets using the the unbounded\n absolutely weakly convergence and applications
• Disjointly Weak Compactness in Banach Lattices
• Generalizations of L- and M-weakly compact operators