Abstract
We construct the category of quotients of \(\mathcal{L}\mathfrak{F}\)-spaces and we show that it is Abelian. This answers a question of L. Waelbroeck from 1990.
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H. Hogbe Nlend: Théorie des Bornologies et Applications. Lect. Notes Math. Vol. 213. Springer-Verlag, Berlin-Heidelberg-New York, 1971. (French.)
A. Grothendieck: Produits Tensoriels Topologiques et Espaces Nucléaires. Mem. Amer. Math. Soc. No. 16. AMS, Providence, 1966.
L. Waelbroeck: Topological Vector Spaces and Algebras. Lect. Notes Math. Vol. 230. Springer-Verlag, Berlin-Heidelberg-New York, 1971.
L. Waelbroeck: Quotient Banach Spaces, Spectral theory 8. Banach Cent. Publ., Warsaw, 1982, pp. 553–562.
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.
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Aqzzouz, B., Nouira, R. The Abelian category of quotients of \(\mathcal{L}\mathfrak{F}\)-spaces. Czech Math J 57, 183–190 (2007). https://doi.org/10.1007/s10587-007-0054-8
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DOI: https://doi.org/10.1007/s10587-007-0054-8