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Smooth points of vector valued function spaces. (English) Zbl 0817.46036

Summary: If \(E\) is a Banach space, then an element \(x\in E\), \(\| x\|=1\) is called smooth if there is a unique \(x^*\in E^*\), \(\| x^* \|=1\) such that \(\langle x^*, x\rangle=1\). The object of this paper is to characterize the smooth points of \(L^ p (I, X)\), \(\ell^ p (X)\), \(1\leq p<\infty\), where \(X\) is some Banach space. Some other related results are presented.

MSC:

46E40 Spaces of vector- and operator-valued functions
46B25 Classical Banach spaces in the general theory
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References:

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