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1999 | 133 | 2 | 163-174
Tytuł artykułu

On Arens-Michael algebras which do not have non-zero injective ⨶-modules

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EN
Abstrakty
EN
A certain class of Arens-Michael algebras having no non-zero injective topological ⨶-modules is introduced. This class is rather wide and contains, in particular, algebras of holomorphic functions on polydomains in $ℂ^n$, algebras of smooth functions on domains in $ℝ^n$, algebras of formal power series, and, more generally, any nuclear Fréchet-Arens-Michael algebra which has a free bimodule Koszul resolution.
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Twórcy
  • Faculty of Mechanics and Mathematics, Moscow State University, Moscow 119899 GSP, Russia, pirkosha@glasnet.ru
Bibliografia
  • [1] S. S. Akbarov, shape The Pontryagin duality in the theory of topological modules, Funktsional. Anal. i Prilozhen. 29 (1995), no. 4, 68-72 (in Russian).
  • [2] R. Engelking, shape General Topology, PWN, Warszawa, 1977.
  • [3] J. Eschmeier and M. Putinar, shape Spectral Decompositions and Analytic Sheaves, Clarendon Press, Oxford, 1996.
  • [4] A. Grothendieck, shape Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
  • [5] A. Ya. Helemskii, shape The Homology of Banach and Topological Algebras, Moscow Univ. Press, 1986 (in Russian); English transl.: Kluwer Acad. Publ., Dordrecht, 1989.
  • [6] A. Ya. Helemskii, shape Banach and Polynormed Algebras: General Theory, Representations, Homology, Nauka, Moscow, 1989 (in Russian); English transl.: Oxford Univ. Press, 1993.
  • [7] A. Ya. Helemskii, shape 31 problems of the homology of the algebras of analysis, in: Linear and Complex Analysis: Problem Book 3, Part I, V. P. Havin and N. K. Nikolski (eds.), Lecture Notes in Math. 1573, Springer, Berlin, 1994, 54-78.
  • [8] MG. Köthe, shape Topological Vector Spaces II, Springer, New York, 1979.
  • [9] A. Yu. Pirkovskii, shape On the non-existence of cofree Fréchet modules over non-normable locally multiplicatively convex Fréchet algebras, Rocky Mountain J. Math., to appear.
  • [10] A. Yu. Pirkovskii, shape On the existence problem for a sufficient family of injective Fréchet modules over non-normable Fréchet algebras, Izv. Ross. Akad. Nauk Ser. Mat. 62 (1998), no. 4, 137-154 (in Russian).
  • [11] H. Schaefer, shape Topological Vector Spaces, Macmillan, New York, 1966.
  • [12] J. L. Taylor, shape Homology and cohomology for topological algebras, Adv. in Math. 9 (1972), 137-182.
  • [13] J. L. Taylor, shape A general framework for a multi-operator functional calculus, ibid., 183-252.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv133i2p163bwm
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