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Property (\(K\)) of Orlicz-Bochner sequence spaces. (Chinese. English summary) Zbl 1438.46019

Summary: In this paper, we investigate the property (\(K\)) of Orlicz-Bochner sequence spaces. Analyzing and combining the generating function \(M\) and properties of the Orlicz-Bochner sequence spaces, when the Banach space \(X\) has the Schur property, we get the sufficient and necessary condition of the property (\(K\)) of Orlicz-Bochner sequence spaces, and then we get a sufficient condition of Orlicz-Bochner sequence spaces with the weak fixed point property.

MSC:

46B20 Geometry and structure of normed linear spaces
46B45 Banach sequence spaces
46E40 Spaces of vector- and operator-valued functions
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