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On uniform Kadec–Klee properties and rotundity in generalized Cesàro sequence spaces. (English) Zbl 1074.46010

Summary: We consider the generalized Cesàro sequence spaces defined by S. Suantai [Georgian Math. J. 10, No. 1, 193–200 (2003; Zbl 1051.46011)] and consider it equipped with the Amemiya norm. The main purpose of this paper is to show that \(\text{ces}_{(p)}\) equipped with the Amemiya norm is rotund and has the uniform Kadec–Klee property.

MSC:

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

Citations:

Zbl 1051.46011
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