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.

中文翻译：

---

Banach Compactness 和 Banach 核运营商

在本文中，我们介绍了（均匀弱）巴拿赫紧集、（均匀弱）巴拿赫紧算子和（均匀弱）巴拿赫核算子的概念，它们推广了 p-紧致集、p-紧致算子和 p-核运营商，分别。研究了基本特性。给出了因式分解和对偶定理。内射和满射包用于显示（均匀弱）巴拿赫紧算子和（均匀弱）巴拿赫核算子的空间是拟巴拿赫算子理想。