| Title:
|
The exactness of the projective limit functor on the category of quotients of Frechet spaces (English) |
| Author:
|
Aqzzouz, Belmesnaoui |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
173-181 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give conditions under which the functor projective limit is exact on the category of quotients of Fréchet spaces of L. Waelbroeck [18]. (English) |
| Keyword:
|
quotient d’espaces de Fréchet |
| Keyword:
|
limite projective |
| MSC:
|
46A04 |
| MSC:
|
46A17 |
| MSC:
|
46M05 |
| MSC:
|
46M15 |
| MSC:
|
46M40 |
| idZBL:
|
Zbl 1174.46036 |
| idMR:
|
MR2402533 |
| . |
| Date available:
|
2009-09-24T11:54:21Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128253 |
| . |
| Reference:
|
[1] B. Aqzzouz and R. Nouira: La catégorie abélienne des quotients de type $\mathcal{LF}$.Czech. Math. J. 57 (2007), 183–190. MR 2309959 |
| Reference:
|
[2] B. Aqzzouz: Une application du Lemme de Mittag-Leffler dans la catégorie des quotients d’espaces de Fréchet. (to appear). |
| Reference:
|
[3] P. Domanski and D. Vogt: A splitting theorem for the space of smooth functions.J. Funct. Anal. 153 (1998), 203–248. MR 1614582, 10.1006/jfan.1997.3177 |
| Reference:
|
[4] P. Domanski and D. Vogt: Distributional complexes split for positive dimensions.J. Reine Angew. Math. 522 (2000), 63–79. MR 1758575 |
| Reference:
|
[5] 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. Zbl 0195.10401, MR 0285849 |
| Reference:
|
[6] A. Grothendieck: Produits tensoriels topologiques et espaces nucléaires.Mem. Amer. Math. Soc. (1966). MR 1609222 |
| Reference:
|
[7] L. Hörmander: The analysis of partial differential operators II.Grundlehren der Mathematischen Wissenschaften Springer-Verlag, Berlin, 1983. |
| Reference:
|
[8] V. P. Palamodov: The projective limit functor in the category of topological linear spaces.Mat. Sb. (N.S.) 75 117 (1968), 567–603. (Russian) MR 0223851 |
| Reference:
|
[9] 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. Zbl 0191.43401, MR 0264197 |
| Reference:
|
[10] V. P. Palamodov: Homological methods in the theory of locally convex spaces.Uspehi Mat. Nauk 26 1 (1971), 3–65. (Russian) Zbl 0247.46070, MR 0293365 |
| Reference:
|
[11] V. P. Palamodov: On a Stein manifold the Dolbeault complex splits in positive dimensions.Mat. Sb. (N.S.) 88 (1972), 287–315. (Russian) MR 0313540 |
| Reference:
|
[12] 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. Zbl 1112.58304, MR 1222219 |
| Reference:
|
[13] F. H. Vasilescu: Spectral theory in quotient Fréchet spaces I.Revue Roumaine de Math. Pures et Appl. 32 (1987), 561–579. Zbl 0665.46058, MR 0900363 |
| Reference:
|
[14] F. H. Vasilescu: Spectral theory in quotient Fréchet spaces II.J. Operator theory 21 (1989), 145–202. Zbl 0782.46005, MR 1002127 |
| Reference:
|
[15] D. Vogt: On the functors $\mathop {\text{Ext}}_{1}(E,F)$ for Fréchet spaces.Studia Math. 85 (1987), 163–197. MR 0887320, 10.4064/sm-85-2-163-197 |
| Reference:
|
[16] L. Waelbroeck: Quotient Banach spaces.Banach Center Publ. Warsaw (1982), 553–562 and 563–571. Zbl 0492.46014, MR 0738315 |
| Reference:
|
[17] 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. Zbl 0633.46071, MR 0849594 |
| Reference:
|
[18] L. Waelbroeck: Quotient Fréchet spaces.Revue Roumaine de Math. Pures et Appl. 34, n. 2 (1989), 171–179. Zbl 0696.46052, MR 1005909 |
| Reference:
|
[19] 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. Zbl 0711.46010, MR 1090139 |
| Reference:
|
[20] J. Wengenroth: Derived Functors in Functional Analysis.Lecture Notes in Math. 1810. Springer-Verlag, Berlin, 2003. Zbl 1031.46001, MR 1977923 |
| . |
