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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_1979_13_2_a0,
     author = {A. V. Bukhvalov},
     title = {Supplement to the paper {``On} the duality of functors generated by spaces of vector-valued functions''},
     journal = {Izvestiya. Mathematics },
     pages = {215--219},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {1979},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a0/}
}
TY  - JOUR
AU  - A. V. Bukhvalov
TI  - Supplement to the paper ``On the duality of functors generated by spaces of vector-valued functions''
JO  - Izvestiya. Mathematics 
PY  - 1979
SP  - 215
EP  - 219
VL  - 13
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a0/
LA  - en
ID  - IM2_1979_13_2_a0
ER  - 
%0 Journal Article
%A A. V. Bukhvalov
%T Supplement to the paper ``On the duality of functors generated by spaces of vector-valued functions''
%J Izvestiya. Mathematics 
%D 1979
%P 215-219
%V 13
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a0/
%G en
%F IM2_1979_13_2_a0
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/

[1] Mityagin B. S., Shvarts A. S., “Funktory v kategoriyakh banakhovykh prostranstv”, Uspekhi matem. nauk, XIX:2(116) (1964), 65–130

[2] Bukhvalov A. V., “O dvoistvennosti funktorov, porozhdaemykh prostranstvami vektor-funktsii”, Izv. AN SSSR. Ser. matem., 39 (1975), 1284–1309 | Zbl

[3] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977 | MR | Zbl

[4] Lozanovskii G. Ya., “O normirovannykh strukturakh s polunepreryvnoi normoi”, Sib. matem. zh., 12:1 (1971), 231–234

[5] Lozanovskii G. Ya., Mekler A. A., “Vpolne lineinye funktsionaly i refleksivnost v normirovannykh lineinykh strukturakh”, Izv. vuzov, matem., 1967, no. 11, 47–53 | MR | Zbl

[6] Arterburn D., Whitley R., “Projections in the space of bounded linear operators”, Pacific J. Math., 15:3 (1965), 739–746 | MR | Zbl

[7] Bukhvalov A. V., “O lokalno vypuklykh prostranstvakh, porozhdennykh slabo kompaktnymi mnozhestvami”, Vestnik LGU, 1973, no. 7, 11–17 | Zbl