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- Title
On Semitransitive Collections of Operators.
- Authors
Bernik, J.; Grunenfelder, L.; Mastnak, M.; Radjavi, H.; Troitsky, V. G.
- Abstract
A collection F of operators on a vector space V is said to be semitransitive if for every pair of nonzero vectors x and y in V there exists a member T of F such that either Tx = y or Ty = x (or both). We study semitransitive algebras and semigroups of operators. One of the main results is that if the underlying field is algebraically closed, then every semitransitive algebra of operators on a space of dimension n contains a nilpotent element of index n. Among other results on semitransitive semigroups, we show that if the rank of nonzero members of such a semigroup acting on an n-dimensional space is a constant k, then k divides n.
- Subjects
OPERATOR algebras; OPERATOR theory; SEMIGROUPS of operators; ALGEBRA; TOPOLOGICAL algebras
- Publication
Semigroup Forum, 2005, Vol 70, Issue 3, p436
- ISSN
0037-1912
- Publication type
Article
- DOI
10.1007/s00233-004-0168-3