We consider $C$-compact orthogonally additive operators in vector lattices. After providing some examples of $C$-compact orthogonally additive operators on a vector lattice with values in a Banach space we show that the set of those operators is a projection band in the Dedekind complete vector lattice of all regular orthogonally additive operators. In second part of the article we introduce a new class of vector lattices, called $C$-complete, and show that any laterally-to-norm continuous $C$-compact orthogonally additive operator from a $C$-complete vector lattice to a Banach space is narrow, which generalizes a result of Pliev and Popov.

中文翻译：

---

关于 C-compact 正交加法算子

我们考虑向量格中的 $C$-compact 正交加法算子。在提供了具有 Banach 空间值的向量点阵上的 $C$-compact 正交加法算子的一些例子之后，我们证明了这些算子的集合是所有规则正交加法算子的 Dedekind 完全向量点阵中的投影带。在文章的第二部分，我们介绍了一类新的向量格，称为 $C$-complete，并展示了从 $C$-完全向量格到Banach 空间是狭窄的，它概括了 Pliev 和 Popov 的结果。