Davidson, K. R. and Power, S. C. and Paulsen, V. I. (1994) Tree algebras, semidiscreteness and dilation theory. Proceedings of the London Mathematical Society, 68 (1). pp. 178-202.Full text not available from this repository.
We introduce a class of finite-dimensional algebras built from a partial order generated as a transitive relation from a finite tree. These algebras, known as tree algebras, have the property that every locally contractive representation has a *-dilation. Furthermore, they satisfy an appropriate analogue of the Sz. Nagy–Foia Commutant Lifting Theorem. Then we define the infinite-dimensional analogue of these algebras in the class of completely distributive CSL algebras. These algebras are shown to have the semidiscreteness and complete compact approximation properties with respect to the class of finite-dimensional tree algebras. Consequently, they also have the property that contractive weak-* continuous representations have *-dilations, and satisfy the Sz. Nagy–Foia Commutant Lifting Theorem.
|Journal or Publication Title:||Proceedings of the London Mathematical Society|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited On:||13 Nov 2008 09:06|
|Last Modified:||14 Aug 2012 15:24|
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