In this article we consider some classes of orthogonally additive operators in Köthe–Bochner spaces in the setting of the theory of lattice-normed spaces and dominated operators. The our first main result asserts that the C -compactness of a dominated orthogonally additive operator $$S:E(X)\rightarrow F(Y)$$ S : E ( X ) → F ( Y ) implies the C -compactness of its exact dominant $$|\!|S|\!|:E\rightarrow F$$ | | S | | : E → F . Then we show that a dominated orthogonally additive operator $$S:E(X)\rightarrow F$$ S : E ( X ) → F from a Köthe–Bochner space to a Banach lattice F with an order continuous norm is narrow if and only if its exact dominant $$|\!|S|\!|:E\rightarrow F$$ | | S | | : E → F is. Finally we prove that every laterally-to-norm continuous dominated orthogonally additive operator from E ( X ) to a sequence Banach lattice F is narrow.

中文翻译：

---

关于 Köthe-Bochner 空间中的正交可加算子

在本文中，我们在格规范空间和支配算子理论的背景下考虑了 Köthe-Bochner 空间中的一些正交加算子类。我们的第一个主要结果断言，支配正交加法算子 $$S:E(X)\rightarrow F(Y)$$S : E ( X ) → F ( Y ) 的 C -compactness 意味着 C -compactness它完全占优势的 $$|\!|S|\!|:E\rightarrow F$$ | | | | | ：E→F。然后我们证明了从 Köthe–Bochner 空间到具有阶连续范数的 Banach 格 F 的占优正交加法算子 $$S:E(X)\rightarrow F$$S:E(X)→F 是窄的，如果和仅当其完全支配 $$|\!|S|\!|:E\rightarrow F$$ | | | | | : E → F 是。最后，我们证明了从 E ( X ) 到序列 Banach 格 F 的每个横向到范数连续支配的正交加算子都是窄的。