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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
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