Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-13T04:05:11.709Z Has data issue: false hasContentIssue false
  • English
  • Français

Biprojectivity and Biflatness for Convolution Algebras of Nuclear Operators

Published online by Cambridge University Press:  20 November 2018

A. Yu. Pirkovskii
A. Yu. Pirkovskii*
Affiliation:
Department of Differential Equations and Functional Analysis Faculty of Science Peoples’ Friendship University of Russia Mikluho-Maklaya 6 117198 Moscow Russia, E-mail: pirkosha@sci.pfu.edu.ru, pirkosha@online.ru
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For a locally compact group $G$, the convolution product on the space $N({{L}^{p}}\ (G))$ of nuclear operators was defined by Neufang [11]. We study homological properties of the convolution algebra $N({{L}^{p}}\ (G))$ and relate them to some properties of the group $G$, such as compactness, finiteness, discreteness, and amenability.

Keywords

46M1046H2543A2016E65
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 3 , 01 September 2004 , pp. 445 - 455
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Dales, H. G., Banach algebras and automatic continuity. Oxford Univ. Press, New York, 2000.Google Scholar
[2] Diestel, J. and Faires, B., On vector measures. Trans. Amer.Math. Soc. 198 (1974), 253–271.Google Scholar
[3] Diestel, J. and Uhl, J. J. Jr., Vector measures. American Mathematical Society, Providence, RI., 1977.Google Scholar
[4] Hewitt, E. and Ross, K. A., Abstract harmonic analysis, Vol. II. Springer-Verlag, Berlin, 1970.Google Scholar
[5] Helemskii, A. Ya., On a method for calculating and estimating the global homological dimension of Banach algebras. Mat. Sbornik 87 (1972), 122–135 (Russian); English transl.: Math. USSR Sb. 16 (1972), 125–138.Google Scholar
[6] Helemskii, A. Ya., Flat Banach modules and amenable algebras. Trudy MMO 47 (1984), 179–218 (Russian); English transl.: Trans. Moscow Math. Soc. 47 (1985), 199–244.Google Scholar
[7] Helemskii, A. Ya., The homology of Banach and topological algebras. Moscow University Press, 1986 (Russian); English transl.: Kluwer Academic Publishers, Dordrecht, 1989.Google Scholar
[8] Helemskii, A. Ya., Banach and polynormed algebras: general theory, representations, homology. Nauka, Moscow, 1989 (Russian); English transl.: Oxford University Press, 1993.Google Scholar
[9] Johnson, B. E., Cohomology in Banach algebras. Mem. Amer. Math. Soc. 127(1972).Google Scholar
[10] Johnson, W. B. and Lindenstrauss, J., Basic concepts in the geometry of Banach spaces, Handbook of the geometry of Banach spaces, Vol. I, 1–84, North-Holland, Amsterdam, 2001.Google Scholar
[11] Neufang, M., Abstrakte harmonische Analyse und Modulhomomorphismen über von Neumann-Algebren. Dissertation zur Erlangung des Grades des Doktors des Naturwissenschaften, Saarbrücken, 2000.Google Scholar
[12] Runde, V., Lectures on amenability. Lecture Notes in Math. 1774, Springer-Verlag, Berlin, 2002.Google Scholar
[13] Selivanov, Yu. V., Biprojective Banach algebras. Izvestia. Akad. Nauk SSSR ser. mat. 43 (1979), 1159–1174; English transl.: Math. USSR Izvestija 15 (1980), 387–399.Google Scholar
[14] Selivanov, Yu. V.,Weak homological bidimension and its values in the class of biflat Banach algebras. Extracta Math. 11 (1996), 348–365.Google Scholar
[15] Selivanov, Yu. V., Superbiprojective and superbiflat Banach algebras. Unpublished manuscript, Odense, 2001.Google Scholar
[16] Wendel, J. G., Left centralizers and isomorphisms of group algebras. Pacific J.Math. 2 (1952), 251–261.Google Scholar
[17] Wojtaszczyk, P., Banach spaces for analysts. Cambridge University Press, Cambridge, 1991.Google Scholar