Supplement to the paper “On the duality of functors generated by spaces of vector-valued functions”

A. V. Bukhvalov


Abstract: 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.

UDC: 513.88+519.47

MSC: Primary 46E40, 46M05; Secondary 46A40

Received: 28.11.1977

 English version: Mathematics of the USSR-Izvestiya, 1979, 13:2, 215–219

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