Recently, the different types of unbounded convergences \((uo, un, uaw, ua w^*)\) in Banach lattices were studied. In this paper, we study the continuous functionals with respect to unbounded convergences. We first characterize the continuity of linear functionals for these convergences. Then we define the corresponding unbounded dual spaces and get their exact form. Based on these results, we discuss order continuity and reflexivity of Banach lattices. Some related results are obtained as well.

中文翻译：

---

Banach格中无界收敛的连续函数

最近，研究了Banach格中不同类型的无界收敛\（（uo，un，uaw，ua w ^ *）\）。在本文中，我们研究了关于无界收敛的连续函数。我们首先描述这些收敛的线性泛函的连续性。然后，我们定义相应的无界对偶空间并获得其精确形式。基于这些结果，我们讨论了Banach格的顺序连续性和自反性。也获得了一些相关结果。