×

zbMATH — the first resource for mathematics

A group of operators G in a space without G-torsion. (English. Russian original) Zbl 0576.06019
Sib. Math. J. 25, 845-849 (1984); translation from Sib. Mat. Zh. 25, No. 6(148), 17-22 (1984).
It is known that if in a linear space \(L_ n(K)\) with group G of operators there exists a G-invariant linear order, then it has no G- torsion. But also examples of a space without G-torsion in which there is no G-invariant order are known. The author obtains in this paper necessary and sufficient conditions for (1) each of the spaces \(L_ n(R)\), \(L_ n(Q)\) with group G of operators to have no G-torsion, and (2) \(L_ n(Q)\) to have a G-invariant linear order.
Reviewer: C.G.Chehata
MSC:
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
47D03 Groups and semigroups of linear operators
20C99 Representation theory of groups
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] V. V. Bludov, ?Example of an unorderable group with strictly isolated identity,? Algebra Logika, No. 11, 619-632 (1972).
[2] R. B. Mura and A. H. Rhemtulla, ?Solvable R*-groups,? Math. Z.,142, No. 3, 293-298 (1975). · Zbl 0295.20036 · doi:10.1007/BF01183052
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.