Rank Distributions on Coarse Spaces and Ideal Structure of Roe Algebras |
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Authors: | Chen Xiaoman; Wang Qin |
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Institution: | Institute of Mathematics, Fudan University Shanghai, 200433, P. R. China xchen{at}fudan.edu.cn
Department of Applied Mathematics, Dong Hua University Shanghai, 200051, P. R. China qwang{at}dhu.edu.cn |
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Abstract: | The notions of controlled truncations for operators in the Roealgebras C* (X) of a coarse space (X, ) with uniformly locallyfinite coarse structure, and rank distributions on (X, ) areintroduced. It is shown that the controlled propagation operatorsin an ideal I of C* (X) are exactly the controlled truncationsof elements in I. It follows that the lattice of the idealsof C* (X) in which controlled propagation operators are denseis isomorphic to the lattice of all rank distributions on (X,). If X is a discrete metric space with Yu's property A, thenthe ideal structure of the Roe algebra C* (X is completely determinedby the rank distributions on X. 2000 Mathematics Subject Classification46L80, 46L89. |
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