English

Transitive spaces of operators

Operator Algebras 2007-06-19 v1

Abstract

We investigate algebraic and topological transitivity and, more generally, k-transitivity for linear spaces of operators. In finite dimensions, we determine minimal dimensions of k-transitive spaces for every k, and find relations between the degree of transitivity of a product or tensor product on the one hand and those of the factors on the other. We present counterexamples to some natural conjectures. Some infinite dimensional analogues are discussed. A simple proof is given of Arveson's result on the weak-operator density of transitive spaces that are masa bimodules.

Keywords

Cite

@article{arxiv.0706.2449,
  title  = {Transitive spaces of operators},
  author = {K. R. Davidson and L. W. Marcoux and H. Radjavi},
  journal= {arXiv preprint arXiv:0706.2449},
  year   = {2007}
}
R2 v1 2026-06-21T08:39:11.911Z