Transitive Spaces of Operators |
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Authors: | Kenneth R Davidson Laurent W Marcoux Heydar Radjavi |
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Institution: | (1) Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L–3G1, Canada |
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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.
Authors partially supported by NSERC grants. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 15A04 47A15 47A16 47L05 |
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