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.
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The authors would like to thank the referee for valuable comments.
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Ju Myung Kim was supported by NRF-2018R1D1A1B07043566 (Korea)
Keun Young Lee was supported by NRF-2017R1C1B5017026 (Korea)
Bentuo Zheng was supported in part by Simons Foundation Grant 585081.
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Kim, J.M., Lee, K.Y. & Zheng, B. Banach Compactness and Banach Nuclear Operators. Results Math 75, 161 (2020). https://doi.org/10.1007/s00025-020-01295-0
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DOI: https://doi.org/10.1007/s00025-020-01295-0