Hostname: page-component-84b7d79bbc-4hvwz Total loading time: 0 Render date: 2024-07-25T22:30:58.112Z Has data issue: false hasContentIssue false
  • English
  • Français

On reducibility of ultrametric almost periodic linear representations

Published online by Cambridge University Press:  18 May 2009

Bertin Diarra
Bertin Diarra
Affiliation:
Mathematiques Pures, Complexe Scientifique Des Cézeaux, 63177 Aubiere Cedex, France Fax: (33) 73.40.70.64 e-mail diarra@ucfma.univ-bpclermont.fr
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.

Let G be a group and K be a complete ultrametric valued field. Let AP(G, K) be the algebra of the generalized almost periodic functions of G in K. We have shown in a previous paper that when AP(G, K) has an invariant mean, then any almost periodic linear representation is quasi-reducible. Here, we show that with the same hypothesis, any topologically irreducible almost periodic linear representation is finite dimensional; also, any almost periodic linear representation is the topological sum of irreducible representations. Furthermore, we obtain a Peter-Weyl theorem for the algebra AP(G, K).

We use the technical tools of Hopf algebra theory.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 1 , January 1995 , pp. 83 - 98
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

REFERENCES

1.Amice, Y., Les nombres p-adiques (P.U.F.-1975).Google Scholar
2.Diana, B.. Algèbres de Hopf et fonctions presque périodiques ultramétriques, to appear in Rivista di Matematica pur a ed applicata n° 16.Google Scholar
3.Diarra, B.. Ultrametric almost periodic linear representations in p-adic Functional Analysis (Editorial Universidad de Santiago, Chile, 1994), 45–55.Google Scholar
4.Gruson, L.. Théorie de Fredholm p-adique, Bull. Soc. Math. France 94 (1966), 67–95.CrossRefGoogle Scholar
5.Gruson, L. and Put., M. van der Banach spaces, Bull. Soc. Math. France, Mémoire 39–40 (1974), 55–100.CrossRefGoogle Scholar
6.Rangan, G. and Saleemullah, M. S.. Banach algebra of p-adic valued almost periodic functions, in p-adic Functionnal Analysis, edited by Bayod, J. M., Kimpe, N. De Grande-De and Martinez-Maurica, J. (Marcel Dekker, New-York-1991), 141–150.Google Scholar
7.Rooij, A. C. M. van: Non-archimedean functional analysis (Marcel Dekker, New York, 1978).Google Scholar
8.Schikhof, W. H.. An approach to p-adic almost periodicity by means of compactoids. Report 8809-Departement of Mathematics, Catholic University (Nijmegen, 1988).Google Scholar
9.Schikhof, W. H.. p-Adic almost periodic functions. Indag. Math. 1 n° 1 (1990), 127–133.CrossRefGoogle Scholar
10.Serre, J.-P.. Endomorphismes complètement continus des espaces de Banach p-adiques Publ. Math. n° 12 (1962) (I.H.E.S. Paris), 69–85.Google Scholar