Semigroups containing proximal linear maps

Abels H, Margulis GA, Soifer GA (1995)
Israel Journal of Mathematics 91(1-3): 1-30.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Abels, HerbertUniBi; Margulis, G.A.; Soifer, G.A.
Abstract / Bemerkung
A linear automorphism of a finite dimensional red vector space V is called proximal if it has a unique eigenvalue-counting multiplicities-of maximal modulus. Goldsheid and Margulis have shown that if a subgroup G of GL(V) contains a proximal element then so does every Zariski dense subsemigroup H of G, provided V considered as a G-module is strongly irreducible. We here show that H contains a finite subset M such that for every g is an element of GL(V) at least one of the elements gamma g, gamma is an element of M, is proximal. We also give extensions and refinements of this result in the following directions: a quantitative version of proximality, reducible representations, several eigenvalues of maximal modulus.
Erscheinungsjahr
1995
Zeitschriftentitel
Israel Journal of Mathematics
Band
91
Ausgabe
1-3
Seite(n)
1-30
ISSN
0021-2172
Page URI
https://pub.uni-bielefeld.de/record/1640057

Zitieren

Abels H, Margulis GA, Soifer GA. Semigroups containing proximal linear maps. Israel Journal of Mathematics. 1995;91(1-3):1-30.
Abels, H., Margulis, G. A., & Soifer, G. A. (1995). Semigroups containing proximal linear maps. Israel Journal of Mathematics, 91(1-3), 1-30. https://doi.org/10.1007/BF02761637
Abels, H., Margulis, G. A., and Soifer, G. A. (1995). Semigroups containing proximal linear maps. Israel Journal of Mathematics 91, 1-30.
Abels, H., Margulis, G.A., & Soifer, G.A., 1995. Semigroups containing proximal linear maps. Israel Journal of Mathematics, 91(1-3), p 1-30.
H. Abels, G.A. Margulis, and G.A. Soifer, “Semigroups containing proximal linear maps”, Israel Journal of Mathematics, vol. 91, 1995, pp. 1-30.
Abels, H., Margulis, G.A., Soifer, G.A.: Semigroups containing proximal linear maps. Israel Journal of Mathematics. 91, 1-30 (1995).
Abels, Herbert, Margulis, G.A., and Soifer, G.A. “Semigroups containing proximal linear maps”. Israel Journal of Mathematics 91.1-3 (1995): 1-30.

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