Reducibility and triangularizability of semitransitive spaces of operators

  title={Reducibility and triangularizability of semitransitive spaces of operators},
  author={J. Bernik and Roman Drnov{\vs}ek and Damjana Kokol Bukovsek and Tomaz Kosir and Matjaz Omladic},
A linear space L of operators on a vector space X is called semitransitive if, given two nonzero vectors x, y in X, there exists an element A in L such that either y=Ax or x=Ay. In this paper we consider semitransitive spaces of operators on a finite dimensional vector space X over an algebraically closed field. In particular, we are interested in the existence of nontrivial invariant subspaces of X for a semitransitive space L. We are able to relate the existence of an invariant subspace for L… CONTINUE READING