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Article

Aqzzouz, B. ; Nouira, R.
La categorie Abelienne des quotients de type ${\mathcal LF}$. (French) [The Abelian category of quotients of ${\mathcal LF}$-spaces]. Czechoslovak Mathematical Journal, vol. 57 (2007), issue 1, pp. 183-190
MSC: 46A13, 46M05, 46M15, 46M40 | MR 2309959 | Zbl 1174.46037
Keywords:
$\scr {L}\Im $-space; foncteur; catégorie abélienne
Summary:
We construct the category of quotients of $\mathcal {L}\Im $-spaces and we show that it is Abelian. This answers a question of L. Waelbroeck from 1990.
References:
[1] H. Hogbe Nlend: Théorie des Bornologies et Applications. Lect. Notes Math. Vol. 213. Springer-Verlag, Berlin-Heidelberg-New York, 1971. (French) MR 0625157
[2] A.  Grothendieck: Produits Tensoriels Topologiques et Espaces Nucléaires. Mem. Amer. Math. Soc. No. 16. AMS, Providence, 1966. MR 1609222
[3] L.  Waelbroeck: Topological Vector Spaces and Algebras. Lect. Notes Math. Vol.  230. Springer-Verlag, Berlin-Heidelberg-New York, 1971. MR 0467234
[4] L.  Waelbroeck: Quotient Banach Spaces, Spectral theory 8. Banach Cent. Publ., Warsaw, 1982, pp. 553–562. MR 0738315
[5] L.  Waelbroeck: Holomorphic functions taking their values in a quotient bornological space. Linear operators in function spaces. Proc. 12th  Int. Conf. Oper. Theory, Timisoara, Rommania, 1988. Oper. Theory, Adv. Appl. 43 (1990), 323–335. MR 1090139
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