Geodesic
Tensor Banach algebras of projective type. II. The $l_1$ case
Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 2, pp. 192-206 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is shown that the tensor Banach functor of projective type $\widehat{\mathscr T}_K$ [1] corresponding to the complete normed field $K$ is quasiidempotent on infinite-dimensional $l_1$ spaces, i.e., $$ \widehat{\mathscr T}_K(\theta_K(\widehat{\mathscr T}_K(l_1(M,K))))\cong\widehat{\mathscr T}_K(l_1(M,K)), $$ where $M$ is an infinite set and $\theta_K$ is the forgetful functor. An $l_1$ realization of the Banach algebra $\widehat{\mathscr T}_K(l_1(M,K))$ is constructed. 
@article{TMF_1992_91_2_a1,
     author = {V. D. Ivashchuk},
     title = {Tensor {Banach} algebras of projective {type.~II.} {The~}$l_1$ case},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {192--206},
     year = {1992},
     volume = {91},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_91_2_a1/}
}
TY  - JOUR
AU  - V. D. Ivashchuk
TI  - Tensor Banach algebras of projective type. II. The $l_1$ case
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1992
SP  - 192
EP  - 206
VL  - 91
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1992_91_2_a1/
LA  - ru
ID  - TMF_1992_91_2_a1
ER  - 
%0 Journal Article
%A V. D. Ivashchuk
%T Tensor Banach algebras of projective type. II. The $l_1$ case
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1992
%P 192-206
%V 91
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1992_91_2_a1/
%G ru
%F TMF_1992_91_2_a1
V. D. Ivashchuk. Tensor Banach algebras of projective type. II. The $l_1$ case. Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 2, pp. 192-206. http://geodesic.mathdoc.fr/item/TMF_1992_91_2_a1/

[1] Ivaschuk V. D., TMF, 91:1 (1992), 17–29 | MR | Zbl

[2] Yakovlev N. V., UMN, 44:5(269) (1989), 185–186 | MR | Zbl

[3] Khelemskii A. Ya., Banakhovy i polinormirovannye algebry: obschaya teoriya, predstavleniya, gomologii, Nauka, M., 1989 | MR

[4] Koblits N., $p$-adicheskie chisla, $p$-adicheskii analiz i dzeta-funktsii, Mir, M., 1981 | MR

[5] Kolmogorov A. H., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1981 | MR

[6] Ivaschuk V. D., TMF, 79:1 (1989), 30–40 | MR

[7] Ivaschuk V. D., TMF, 84:1 (1990), 13–22 | MR | Zbl

[8] Grothendieck A., Mem. Amer. Math. Soc., 1955, no. 16, 1–140 | MR

[9] Burbaki N., Teoriya mnozhestv, Mir, M., 1965

[10] Kuratovskii K., Mostovskii A., Teoriya mnozhestv, Mir, M., 1970 | MR

[11] Ingleton A. W., Proc. Cambr. Phil. Soc., 48 (1952), 41–45 | DOI | MR | Zbl

[12] Monna A. F., Analyse non-archimédienne, Springer-Verlag, Berlin–Heidelberg–New York, 1970 | MR | Zbl