RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 1971, Volume 26, Issue 1(157), Pages 3–65 (Mi umn5165)  

This article is cited in 33 scientific papers (total in 33 papers)

Homological methods in the theory of locally convex spaces

V. P. Palamodov


Abstract: This paper deals with the categories of direct and inverse countable spectra of locally convex spaces and with the functors of inductive and projective limits defined on these categories. We study the homological properties of such functors, introduce their satellites, and search for conditions for these satellites to vanish. We then apply the accumulated information about the functors of the limiting processes to certain problems in the theory of locally convex spaces: topological properties of a locally convex inductive limit, the homomorphism of the adjoint operator, the possibility of extending and lifting a map and the properties of the augmentation functor. We also consider examples of certain “pathologies”.

Full text: PDF file (7585 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1971, 26:1, 1–64

Bibliographic databases:

UDC: 513.83
MSC: 46M15, 46A03, 46A13, 46M40
Received: 04.05.1970

Citation: V. P. Palamodov, “Homological methods in the theory of locally convex spaces”, Uspekhi Mat. Nauk, 26:1(157) (1971), 3–65; Russian Math. Surveys, 26:1 (1971), 1–64

Citation in format AMSBIB
\Bibitem{Pal71}
\by V.~P.~Palamodov
\paper Homological methods in the theory of locally convex spaces
\jour Uspekhi Mat. Nauk
\yr 1971
\vol 26
\issue 1(157)
\pages 3--65
\mathnet{http://mi.mathnet.ru/umn5165}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=293365}
\zmath{https://zbmath.org/?q=an:0247.46070}
\transl
\jour Russian Math. Surveys
\yr 1971
\vol 26
\issue 1
\pages 1--64
\crossref{https://doi.org/10.1070/RM1971v026n01ABEH003815}


Linking options:
  • http://mi.mathnet.ru/eng/umn5165
  • http://mi.mathnet.ru/eng/umn/v26/i1/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. R. Volevich, S. G. Gindikin, “The cauchy problem and other related problems for convolution equations”, Russian Math. Surveys, 27:4 (1972), 71–160  mathnet  crossref  mathscinet  zmath
    2. V. P. Palamodov, “On a Stein manifold the Dolbeault complex splits in positive dimensions”, Math. USSR-Sb., 17:2 (1972), 289–316  mathnet  crossref  mathscinet  zmath
    3. D. I. Gurevich, “Generalized bases in certain rings of holomorphic functions”, Math. USSR-Izv., 6:3 (1972), 564–578  mathnet  crossref  mathscinet  zmath
    4. V. A. Geiler, “Projective objects in the category of locally convex spaces”, Funct. Anal. Appl., 6:2 (1972), 149–150  mathnet  crossref  mathscinet  zmath
    5. A. E. Merzon, “On the covering of bounded sets in locally convex spaces”, Funct. Anal. Appl., 6:4 (1972), 335–336  mathnet  crossref  mathscinet  zmath
    6. V. S. Retakh, “Zamechanie o funktore Ext v lokalno vypuklykh prostranstvakh”, UMN, 31:4(190) (1976), 271–272  mathnet  mathscinet  zmath
    7. V. V. Zharinov, “Compact families of locally convex topological vector spaces, Fréchet–Schwartz and dual Fréchet–Schwartz spaces”, Russian Math. Surveys, 34:4 (1979), 105–143  mathnet  crossref  mathscinet  zmath
    8. V. V. Zharinov, “Fourier ultrahyperfunctions”, Math. USSR-Izv., 16:3 (1981), 479–511  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. A. Ya. Helemskii, “Homological methods in Taylor's holomorphic calculus of several operators in a Banach space”, Russian Math. Surveys, 36:1 (1981), 139–192  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. V. A. Smirnov, Chan Khuen, “On the funktor Ext in the category of linear topological spases”, Math. USSR-Izv., 36:1 (1991), 199–210  mathnet  crossref  mathscinet  zmath  adsnasa
    11. Klaus D. Bierstedt, José Bonet, “Weighted (LF)-spaces of Continuous Functions”, Math Nachr, 165:1 (1994), 25  crossref  mathscinet  zmath  isi
    12. Jochen Wengenroth, “Weighted (LF)-spaces of measurable functions”, Results. Math, 32:1-2 (1997), 169  crossref
    13. Victor P. Palamodov, “Holomorphic synthesis of monogenic functions of several quaternionic variables”, J Anal Math, 78:1 (1999), 177  crossref  mathscinet  zmath  isi  elib
    14. Fabienne Prosmans, “Derived Projective Limits of Topological Abelian Groups”, Journal of Functional Analysis, 162:1 (1999), 135  crossref
    15. M. A. Soloviev, “Lorentz-Covariant Ultradistributions, Hyperfunctions, and Analytic Functionals”, Theoret. and Math. Phys., 128:3 (2001), 1252–1270  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. M. A. Soloviev, “Two classes of generalized functions used in nonlocal field theory”, Theoret. and Math. Phys., 143:2 (2005), 651–663  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    17. Yu. F. Korobeinik, “O primenenii teorii vozmuschenii normalno razreshimykh operatorov k nekotorym klassam operatorov v kompleksnoi oblasti”, Vladikavk. matem. zhurn., 7:2 (2005), 64–77  mathnet  mathscinet  elib
    18. Karl-Hermann Neeb, “Towards a Lie theory of locally convex groups”, Jpn J Math, 1:2 (2006), 291  crossref  mathscinet  zmath  isi
    19. M. A. Soloviev, “Decomposition theorems and kernel theorems for a class of functional spaces”, Izv. Math., 70:5 (2006), 1051–1076  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    20. Z.A.. Lykova, “Cyclic-type cohomology of strict inductive limits of Fréchet algebras”, Journal of Pure and Applied Algebra, 205:3 (2006), 471  crossref
    21. Oǧuz Varol, “A generalization of a theorem of A. Grothendieck”, Math Nachr, 280:3 (2007), 313  crossref  mathscinet  zmath  isi
    22. Ya. A. Kopylov, V. I. Kuz'minov, “The Ker-Coker-sequence and its generalization in some classes of additive categories”, Siberian Math. J., 50:1 (2009), 86–95  mathnet  crossref  mathscinet  isi  elib  elib
    23. Ya. A. Kopylov, “The five- and nine-lemmas in P-semi-abelian categories”, Siberian Math. J., 50:5 (2009), 867–873  mathnet  crossref  mathscinet  isi  elib
    24. Joaquín Motos, María Jesús Planells, Jairo Villegas G, “Some embedding theorems for Hörmander–Beurling spaces”, Journal of Mathematical Analysis and Applications, 364:2 (2010), 473  crossref
    25. Domanski P., “Real Analytic Parameter Dependence of Solutions of Differential Equations”, Rev. Mat. Iberoam., 26:1 (2010), 175–238  isi
    26. Ya. A. Kopylov, “The Kuz'minov–Shvedov addition lemma in a quasi-abelian category”, J. Math. Sci., 186:3 (2012), 426–437  mathnet  crossref
    27. Ya. A. Kopylov, “On the homology sequence in a $P$-semi-abelian category”, Sib. elektron. matem. izv., 9 (2012), 190–200  mathnet
    28. Yaroslav A. Kopylov, “The Two-Square Lemma and the connecting morphism in a preabelian category”, Zhurn. SFU. Ser. Matem. i fiz., 5:3 (2012), 316–325  mathnet
    29. A. Yu. Pirkovskii, “Homological dimensions and Van den Bergh isomorphisms for nuclear Fréchet algebras”, Izv. Math., 76:4 (2012), 702–759  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    30. E. I. Smirnov, “Using homological methods on the base of iterated spectra in functional analysis”, Vladikavk. matem. zhurn., 14:4 (2012), 73–82  mathnet
    31. Domanski P., “Notes on Real Analytic Functions and Classical Operators”, Topics in Complex Analysis and Operator Theory, Contemporary Mathematics, 561, eds. Blasco O., Bonet J., Calabuig J., Jornet D., Amer Mathematical Soc, 2012, 3–47  crossref  isi
    32. Félix Cabello Sánchez, Jesús Castillo, Nigel Kalton, “Complex interpolation and twisted twisted Hilbert spaces”, Pacific J. Math, 276:2 (2015), 287  crossref
    33. Bogachev V. Smolyanov O., “Topological Vector Spaces and Their Applications”, Topological Vector Spaces and Their Applications, Springer Monographs in Mathematics, Springer, 2017, 1–456  crossref  isi
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:533
    Full text:215
    References:32
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019