## On the $$H$$-property of some Banach sequence spaces.(English)Zbl 1115.46012

Summary: We define a generalized Cesàro sequence space $$\text{ces}(p)$$ and consider it equipped with the Luxemburg norm under which it is a Banach space. We show that the space $$\text{ces}(p)$$ possesses property $$(H)$$ and property $$(G)$$, and it is rotund, where $$p = (p_k)$$ is a bounded sequence of positive numbers with $$p_k > 1$$ for all $$k \in \mathbb N$$.

### MSC:

 46B45 Banach sequence spaces 46B20 Geometry and structure of normed linear spaces

### Keywords:

property $$(G)$$; Cesàro sequence spaces; Luxemburg norm
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