2007/06/16 by K. R. Davidson, Kenneth R. Davidson, Laurent W. Marcoux +6
Mathematics · #15A04 #47A15 #47A16 #47L05 #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Rings, Modules, and Algebras #math.OA #msc:15A04 #msc:47A15 #msc:47A16 #msc:47L05
paper · pdf · doi:10.48550/arxiv.0706.2449
23 pages
arxiv created 2007/06/16 · openalex publication_date 2007/06/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.