Coarsely invariant Hilbert spaces over infinite connected graphs

Qin Wang

Coarsely invariant Hilbert spaces over infinite connected graphs

Qin Wang^*

^*此作品的通讯作者

Donghua University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

We study a Hilbert space H_V 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 H_V as a closed subspace, and that the inner product structure of H_V is topologically invariant under uniform coarsening of the graph. We also discuss the functorial properties of these Hilbert spaces.

源语言	英语
页（从-至）	71-75
页数	5
期刊	Journal of Donghua University (English Edition)
卷	19
期	1
出版状态	已出版 - 3月 2002
已对外发布	是

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N2 - We study 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.

AB - We study 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.

KW - Coarse geometry

KW - Expanding graph

KW - Hilbert space

KW - Infinite graph

UR - https://www.scopus.com/pages/publications/0036521052

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AN - SCOPUS:0036521052

SN - 1672-5220

VL - 19

SP - 71

EP - 75

JO - Journal of Donghua University (English Edition)

JF - Journal of Donghua University (English Edition)

IS - 1

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Coarsely invariant Hilbert spaces over infinite connected graphs

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