Transitive spaces of operators

Details Transitive spaces of operators Transitive spaces of operators

2007-06-16

arxiv.org/abs/0706.2449v1

Mathematics

Operator Algebras

23 pages

Scientific paper

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.

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