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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 5, Pages 923–927 (Mi izv1884)  

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.

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

Bibliographic databases:

UDC: 513.88+519.47
MSC: Primary 46E40, 46M05; Secondary 46A40
Received: 28.11.1977

Citation: A. V. Bukhvalov, “Supplement to the paper “On the duality of functors generated by spaces of vector-valued functions””, Izv. Akad. Nauk SSSR Ser. Mat., 42:5 (1978), 923–927; Math. USSR-Izv., 13:2 (1979), 215–219

Citation in format AMSBIB
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\by A.~V.~Bukhvalov
\paper Supplement to the paper ``On the duality of functors generated by spaces of vector-valued functions''
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 5
\pages 923--927
\mathnet{http://mi.mathnet.ru/izv1884}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=513907}
\zmath{https://zbmath.org/?q=an:0418.46056|0391.46052}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 2
\pages 215--219
\crossref{https://doi.org/10.1070/IM1979v013n02ABEH002040}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JD23800001}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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