The exactness of the projective limit functor on the category of quotients of Frechet spaces

Belmesnaoui Aqzzouz

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 1, page 173-181
  • ISSN: 0011-4642

Abstract

top
We give conditions under which the functor projective limit is exact on the category of quotients of Fréchet spaces of L. Waelbroeck [18].

How to cite

top

Aqzzouz, Belmesnaoui. "The exactness of the projective limit functor on the category of quotients of Frechet spaces." Czechoslovak Mathematical Journal 58.1 (2008): 173-181. <http://eudml.org/doc/31206>.

@article{Aqzzouz2008,
abstract = {We give conditions under which the functor projective limit is exact on the category of quotients of Fréchet spaces of L. Waelbroeck [18].},
author = {Aqzzouz, Belmesnaoui},
journal = {Czechoslovak Mathematical Journal},
keywords = {quotient d’espaces de Fréchet; limite projective; quotients of Fréchet spaces; projective limit},
language = {eng},
number = {1},
pages = {173-181},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The exactness of the projective limit functor on the category of quotients of Frechet spaces},
url = {http://eudml.org/doc/31206},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Aqzzouz, Belmesnaoui
TI - The exactness of the projective limit functor on the category of quotients of Frechet spaces
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 1
SP - 173
EP - 181
AB - We give conditions under which the functor projective limit is exact on the category of quotients of Fréchet spaces of L. Waelbroeck [18].
LA - eng
KW - quotient d’espaces de Fréchet; limite projective; quotients of Fréchet spaces; projective limit
UR - http://eudml.org/doc/31206
ER -

References

top
  1. La catégorie abélienne des quotients de type ℒℱ , Czech. Math. J. 57 (2007), 183–190. (2007) MR2309959
  2. Une application du Lemme de Mittag-Leffler dans la catégorie des quotients d’espaces de Fréchet, (to appear). (to appear) 
  3. 10.1006/jfan.1997.3177, J. Funct. Anal. 153 (1998), 203–248. (1998) MR1614582DOI10.1006/jfan.1997.3177
  4. Distributional complexes split for positive dimensions, J. Reine Angew. Math. 522 (2000), 63–79. (2000) MR1758575
  5. 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. (1970) Zbl0195.10401MR0285849
  6. Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. (1966). (1966) MR1609222
  7. The analysis of partial differential operators II, Grundlehren der Mathematischen Wissenschaften Springer-Verlag, Berlin, 1983. (1983) 
  8. The projective limit functor in the category of topological linear spaces, Mat. Sb. (N.S.) 75 117 (1968), 567–603. (Russian) (1968) MR0223851
  9. 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. (1970) Zbl0191.43401MR0264197
  10. Homological methods in the theory of locally convex spaces, Uspehi Mat. Nauk 26 1 (1971), 3–65. (Russian) (1971) Zbl0247.46070MR0293365
  11. On a Stein manifold the Dolbeault complex splits in positive dimensions, Mat. Sb. (N.S.) 88 (1972), 287–315. (Russian) (1972) MR0313540
  12. A criterion for splitness of differential complexes with constant coefficients, Geometric and Algebraic aspects in Several Complex Variables, AMS, 1991, pp. 265-291. (1991) Zbl1112.58304MR1222219
  13. Spectral theory in quotient Fréchet spaces I, Revue Roumaine de Math. Pures et Appl. 32 (1987), 561–579. (1987) Zbl0665.46058MR0900363
  14. Spectral theory in quotient Fréchet spaces II, J. Operator theory 21 (1989), 145–202. (1989) Zbl0782.46005MR1002127
  15. 10.4064/sm-85-2-163-197, Studia Math. 85 (1987), 163–197. (1987) MR0887320DOI10.4064/sm-85-2-163-197
  16. Quotient Banach spaces, Banach Center Publ. Warsaw (1982), 553–562 and 563–571. (1982) Zbl0492.46014MR0738315
  17. The category of quotient bornological spaces, J.A. Barroso (ed.), Aspects of Mathematics and its Applications, Elsevier Sciences Publishers B.V. (1986), 873–894. (1986) Zbl0633.46071MR0849594
  18. Quotient Fréchet spaces, Revue Roumaine de Math. Pures et Appl. 34, n. 2 (1989), 171–179. (1989) Zbl0696.46052MR1005909
  19. 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. (1990) Zbl0711.46010MR1090139
  20. Derived Functors in Functional Analysis, Lecture Notes in Math. 1810. Springer-Verlag, Berlin, 2003. (2003) Zbl1031.46001MR1977923

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.