Non-$$l_n^{(1)}$$ point and uniformly non-$$l_n^{(1)}$$ point of Orlicz–Bochner function spaces

Abstract

Let $$L_M$$ be an Orlicz function space endowed with the Orlicz norm or the Luxemburg norm, and let X be a Banach space. In this paper we characterize the non-$$l_n^{(1)}$$ point and the uniformly non-$$l_{n}^{(1)}$$ point of Orlicz–Bochner function space $$L_M(\mu ,X)$$. As the immediate consequences some criteria for non-square point and uniformly non-square point of $$L_M(\mu ,X)$$ are obtained.