Deeb, W.; Khalil, R. Smooth points of vector valued function spaces. (English) Zbl 0817.46036 Rocky Mt. J. Math. 24, No. 2, 505-512 (1994). 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. Cited in 4 Documents MSC: 46E40 Spaces of vector- and operator-valued functions 46B25 Classical Banach spaces in the general theory Keywords:vector valued function spaces; smooth points PDFBibTeX XMLCite \textit{W. Deeb} and \textit{R. Khalil}, Rocky Mt. J. Math. 24, No. 2, 505--512 (1994; Zbl 0817.46036) Full Text: DOI References: [1] W. Deeb and R. Khalil, Exposed and smooth points of some classes of operators in \(L(l^p)\) , J. Funct. Anal. 103 (1992), 217-228. · Zbl 0807.47031 · doi:10.1016/0022-1236(92)90120-8 [2] W. Deeb and D. Hussain, The dual of \(L(f)\) spaces , Dirasat 6 (1979), 71-84. [3] J. Diestel and J.R. Ohl, Vector measures , Math. Surveys Monographs 15 , 1977. · Zbl 0369.46039 [4] J.R. Holub, On the metric geometric of ideals of operators on Hilbert spaces , Math. Ann. 201 (1973), 157-163. · Zbl 0234.47045 · doi:10.1007/BF01359793 [5] W.A. Light and E.W. Cheney, Approximation theory in tensor product spaces , Lecture Notes in Math. 1169 . · Zbl 0575.41001 [6] I. Singer, Sur la meilleure approximation des fonctions abstracts continues à valeurs dans un espace de Banach , Riv. Mat. Pura Appl. 11 (1957), 245-262. · Zbl 0087.31602 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.