Banach Compactness and Banach Nuclear Operators

Authors

Ju Myung Kim, Sejong UniversityFollow
Keun Young Lee, Sejong University
Bentuo Zheng, University of MemphisFollow

Abstract

In this paper, we introduce the notion of (uniformly weakly) Banach-compact sets, (uniformly weakly) Banach-compact operators and (uniformly weakly) Banach-nuclear operators which generalize p-compact sets, p-compact operators and p-nuclear operators, respectively. Fundamental properties are investigated. Factorizations and duality theorems are given. Injective and surjective hulls are used to show the spaces of (uniformly weakly) Banach-compact operators and (uniformly weakly) Banach-nuclear operators are quasi Banach operator ideals.

Publication Title

Results in Mathematics

Recommended Citation

Kim, J., Lee, K., & Zheng, B. (2020). Banach Compactness and Banach Nuclear Operators. Results in Mathematics, 75 (4) https://doi.org/10.1007/s00025-020-01295-0