Abstract
We give conditions under which the functor projective limit is exact on the category of quotients of Fréchet spaces of L.Waelbroeck [18].
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B. Aqzzouz and R. Nouira: La catégorie abélienne des quotients de type \( \mathcal{L}\mathcal{F} \). Czech. Math. J. 57 (2007), 183–190.
B. Aqzzouz: Une application du Lemme de Mittag-Leffler dans la catégorie des quotients d’espaces de Fréchet. To appear in Math. Bohem. 2008.
P. Domanski and D. Vogt: A splitting theorem for the space of smooth functions. J. Funct. Anal. 153 (1998), 203–248.
P. Domanski and D. Vogt: Distributional complexes split for positive dimensions. J. Reine Angew. Math. 522 (2000), 63–79.
L. Ehrenpreis: Fourier analysis in several complex variables. Pure and Applied Mathematics, Vol. XVII, Wiley-Interscience Publishers A Division of John Wiley & Sons, New York-London-Sydney, 1970.
A. Grothendieck: Produits tensoriels topologiques et espaces nucléaires. Mem. Amer. Math. Soc. (1966).
L. Hörmander: The analysis of partial differential operators II. Grundlehren der Mathematischen Wissenschaften Springer-Verlag, Berlin, 1983.
V. P. Palamodov: The projective limit functor in the category of topological linear spaces. Mat. Sb. (N.S.) 75 117 (1968), 567–603. (In Russian.)
V. P. Palamodov: Linear differential operators with constant coefficients. Translated from the Russian by A. A. Brown. Die Grundlehren der mathematischen Wissenschaften, Band 168 Springer-Verlag, New York-Berlin, 1970.
V. P. Palamodov: Homological methods in the theory of locally convex spaces. Uspehi Mat. Nauk 26 1 (1971), 3–65. (In Russian.)
V. P. Palamodov: On a Stein manifold the Dolbeault complex splits in positive dimensions. Mat. Sb. (N.S.) 88 (1972), 287–315. (In Russian.)
V. P. Palamodov: A criterion for splitness of differential complexes with constant coefficients. Geometric and Algebraic aspects in Several Complex Variables, AMS, 1991, pp. 265–291.
F. H. Vasilescu: Spectral theory in quotient Fréchet spaces I. Revue Roumaine de Math. Pures et Appl. 32 (1987), 561–579.
F. H. Vasilescu: Spectral theory in quotient Fréchet spaces II. J. Operator theory 21 (1989), 145–202.
D. Vogt: On the functors Ext1(E, F) for Fréchet spaces. Studia Math. 85 (1987), 163–197.
L. Waelbroeck: Quotient Banach spaces. Banach Center Publ. Warsaw (1982), 553–562 and 563–571.
L. Waelbroeck: The category of quotient bornological spaces. J. A. Barroso (ed.), Aspects of Mathematics and its Applications, Elsevier Sciences Publishers B. V. (1986), 873–894.
L. Waelbroeck: Quotient Fréchet spaces. Revue Roumaine de Math. Pures et Appl. 34, n. 2 (1989), 171–179.
L. Waelbroeck: Holomorphic Functions taking their values in a quotient bornological space. Linear operators in function spaces, 12th Int. Conf. Oper. Theory, Timisoara (Rom.) 1988, Oper. Theory, Adv. Appl. 43 (1990), 323–335.
J. Wengenroth: Derived Functors in Functional Analysis. Lecture Notes in Math. 1810. Springer-Verlag, Berlin, 2003.
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Aqzzouz, B. The exactness of the projective limit functor on the category of quotients of Frechet spaces. Czech Math J 58, 173–181 (2008). https://doi.org/10.1007/s10587-008-0012-0
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DOI: https://doi.org/10.1007/s10587-008-0012-0