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

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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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     author = {A. V. Bukhvalov},
     title = {Supplement to the paper {``On} the duality of functors generated by spaces of vector-valued functions''},
     journal = {Izvestiya. Mathematics },
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     volume = {13},
     number = {2},
     year = {1979},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a0/}
}
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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/