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

A. Pirkovskii

Studia Mathematica (1999)

  • Volume: 133, Issue: 2, page 163-174
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Pirkovskii, A.. "On Arens-Michael algebras which do not have non-zero injective ⨶-modules." Studia Mathematica 133.2 (1999): 163-174. <http://eudml.org/doc/216611>.

@article{Pirkovskii1999,
abstract = {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.},
author = {Pirkovskii, A.},
journal = {Studia Mathematica},
keywords = {Arens-Michael algebras; non-zero injective topological -modules; algebras of holomorphic functions on polydomains; algebras of smooth functions on domains; formal power series; nuclear Fréchet-Arens-Michael algebra; bimodule Koszul resolution},
language = {eng},
number = {2},
pages = {163-174},
title = {On Arens-Michael algebras which do not have non-zero injective ⨶-modules},
url = {http://eudml.org/doc/216611},
volume = {133},
year = {1999},
}

TY - JOUR
AU - Pirkovskii, A.
TI - On Arens-Michael algebras which do not have non-zero injective ⨶-modules
JO - Studia Mathematica
PY - 1999
VL - 133
IS - 2
SP - 163
EP - 174
AB - 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.
LA - eng
KW - Arens-Michael algebras; non-zero injective topological -modules; algebras of holomorphic functions on polydomains; algebras of smooth functions on domains; formal power series; nuclear Fréchet-Arens-Michael algebra; bimodule Koszul resolution
UR - http://eudml.org/doc/216611
ER -

References

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  1. [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. [2] R. Engelking, shape General Topology, PWN, Warszawa, 1977. 
  3. [3] J. Eschmeier and M. Putinar, shape Spectral Decompositions and Analytic Sheaves, Clarendon Press, Oxford, 1996. 
  4. [4] A. Grothendieck, shape Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955). 
  5. [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. [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. [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. [8] MG. Köthe, shape Topological Vector Spaces II, Springer, New York, 1979. 
  9. [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. [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. [11] H. Schaefer, shape Topological Vector Spaces, Macmillan, New York, 1966. 
  12. [12] J. L. Taylor, shape Homology and cohomology for topological algebras, Adv. in Math. 9 (1972), 137-182. Zbl0271.46040
  13. [13] J. L. Taylor, shape A general framework for a multi-operator functional calculus, ibid., 183-252. Zbl0271.46041

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