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Some properties of \(l^{p}(A,X)\) spaces. (English) Zbl 1168.46301

Summary: We provide a representation of elements of the space \(l^{p}(A,X)\) for a locally convex space \(X\) and \(1\leq p<\infty \) and determine its continuous dual for a normed space \(X\) and \(1<p<\infty \). In particular, we study the extension and characterization of isometries on \(l^{p}(\mathbb N,X)\), when \(X\) is a normed space with an unconditional basis and with a symmetric norm.

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
46B45 Banach sequence spaces
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