Transitive Spaces of Operators

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• 作者：Kenneth R. Davidson ; Laurent W. Marcoux and Heydar Radjavi
• 关键词：Transitive subspace ; k ; transitive ; k ; separating
• 刊名：Integral Equations and Operator Theory
• 出版年：2008
• 出版时间：June, 2008
• 年：2008
• 卷：61
• 期：2
• 页码：187-210
• 全文大小：288.7 KB

文摘

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.