Coarsely invariant Hilbert spaces over infinite connected graphs

Qin Wang

Coarsely invariant Hilbert spaces over infinite connected graphs

Qin Wang^*

^*Corresponding author for this work

Donghua University

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	71-75
Number of pages	5
Journal	Journal of Donghua University (English Edition)
Volume	19
Issue number	1
State	Published - Mar 2002
Externally published	Yes

Keywords

Coarse geometry
Expanding graph
Hilbert space
Infinite graph

Cite this

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abstract = "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.",

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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

M3 - 文章

AN - SCOPUS:0036521052

SN - 1672-5220

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EP - 75

JO - Journal of Donghua University (English Edition)

JF - Journal of Donghua University (English Edition)

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Coarsely invariant Hilbert spaces over infinite connected graphs

Abstract

Keywords

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