In this paper, we introduce the E-approximation property and the $$E^u$$ -approximation property which generalize Sinha and Karn’s p-approximation property. Characterizations of these properties are given parallel to Lima and Oja’s results on the strong approximation property and the weak bounded approximation property. Representation theorems for the dual of $${\mathcal {L}} (X, Y)$$ under the topology of uniform convergence on E-compact sets and $$E^u$$ -compact sets are also provided. As an application, the representations are used to generalize the main theorem of Choi and Kim in [1]. These results build up fundamental bases for future investigations of these properties.

中文翻译：

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E 近似属性

在本文中，我们介绍了 E 逼近性质和 $$E^u$$ - 逼近性质，它们概括了 Sinha 和 Karn 的 p 逼近性质。这些属性的表征与 Lima 和 Oja 在强逼近属性和弱有界逼近属性上的结果并行给出。还提供了在 E-compact 集和 $$E^u$$ -compact 集上一致收敛拓扑下 $${\mathcal {L}} (X, Y)$$ 对偶的表示定理。作为一个应用，这些表示被用来概括 [1] 中 Choi 和 Kim 的主要定理。这些结果为未来对这些特性的研究奠定了基础。