| Coarsely Invariant Hilbert Spaces over Infinite Connected Graphs |
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| 作者姓名： | 王勤 |
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| 作者单位： | WANG QinDepartment of Applied Mathematics，Dong Hua University，Shanghai，200051 |
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| 基金项目： | This research is supported by the NSF from Shanghai Science and Technology Commission, No.01ZA14003. |
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| 摘 要： | We study in this paper a Hilbert space HV associated with the coarse geometry of an infinite connected graph X(V,E) with vertex set V and edge set E. We show that X( V, E) is uniformly expanding if and only if l2( V) can be continuously included in HV as a closed subspace, and that the inner product structure of HV is topologically invariant under uniform coarsening of the graph. We also discuss the functorial properties of these Hilbert spaces.
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Coarsely Invariant Hilbert Spaces over Infinite Connected Graphs |
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| WANG Qin.Coarsely Invariant Hilbert Spaces over Infinite Connected Graphs[J].Journal of Donghua University,2002,19(1). |
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| Authors: | WANG Qin |
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| Abstract: | We study in this paper a Hilbert space HV associated with the coarse geometry of an infinite connected graph X(V,E) with vertex set V and edge set E. We show that X( V, E) is uniformly expanding if and only if l2( V) can be continuously included in HV as a closed subspace, and that the inner product structure of HV is topologically invariant under uniform coarsening of the graph. We also discuss the functorial properties of these Hilbert spaces. |
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| Keywords: | Infinite graph coarse geometry Hilbert space expanding graph |
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