Geodesic
Supplement to the paper “On the duality of functors generated by spaces of vector-valued functions”
Izvestiya. Mathematics, Tome 13 (1979) no. 2, pp. 215-219 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $E$ be a Banach space of measurable functions, and $X$ a Banach space. It is known that $E\otimes X$ is dense in the space $E(X)$ of vector-valued functions if the condition (A) holds: $(e_n\downarrow0)\Rightarrow(\|e_n\|\to0)$. The necessity of this condition was shown in the paper cited in the title (RZhMat., 1976, 5B740) under the assumption that $X$ contains a complemented infinite-dimensional subspace with unconditional basis. In the present paper the requirement of the existence of such a subspace is removed. Also, an error in the earlier paper is corrected. Bibliography: 7 titles. 
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A. V. Bukhvalov. Supplement to the paper “On the duality of functors generated by spaces of vector-valued functions”. Izvestiya. Mathematics, Tome 13 (1979) no. 2, pp. 215-219. http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a0/

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