Ghost ideals in uniform Roe algebras of coarse spaces

Xiaoman Chen; Qin Wang

doi:10.1007/s00013-005-1189-1

Ghost ideals in uniform Roe algebras of coarse spaces

Xiaoman Chen^*
, Qin Wang

^*Corresponding author for this work

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

12 Scopus citations

Abstract

Let C_u*(X) be the uniform Roe algebra of a coarse space X with uniformly locally finite coarse structure. We show that an operator G in C_u*(X) is a ghost element if and only if the finite propagation operators in the principal ideal 〈G〉 are all compact operators. In contrast, if X is a discrete metric space with Yu's property (A), then any ideal in C_u*(X) is the closure of the finite propagation operators in the ideal.

Original language	English
Pages (from-to)	519-526
Number of pages	8
Journal	Archiv der Mathematik
Volume	84
Issue number	6
DOIs	https://doi.org/10.1007/s00013-005-1189-1
State	Published - Jun 2005
Externally published	Yes

Access to Document

10.1007/s00013-005-1189-1

Cite this

@article{66f4bba8f0a54ad29efb9bcdd2b18abd,

title = "Ghost ideals in uniform Roe algebras of coarse spaces",

abstract = "Let Cu*(X) be the uniform Roe algebra of a coarse space X with uniformly locally finite coarse structure. We show that an operator G in Cu*(X) is a ghost element if and only if the finite propagation operators in the principal ideal 〈G〉 are all compact operators. In contrast, if X is a discrete metric space with Yu's property (A), then any ideal in Cu*(X) is the closure of the finite propagation operators in the ideal.",

author = "Xiaoman Chen and Qin Wang",

year = "2005",

month = jun,

doi = "10.1007/s00013-005-1189-1",

language = "英语",

volume = "84",

pages = "519--526",

journal = "Archiv der Mathematik",

issn = "0003-889X",

publisher = "Birkhauser Verlag Basel",

number = "6",

}

TY - JOUR

T1 - Ghost ideals in uniform Roe algebras of coarse spaces

AU - Chen, Xiaoman

AU - Wang, Qin

PY - 2005/6

Y1 - 2005/6

N2 - Let Cu*(X) be the uniform Roe algebra of a coarse space X with uniformly locally finite coarse structure. We show that an operator G in Cu*(X) is a ghost element if and only if the finite propagation operators in the principal ideal 〈G〉 are all compact operators. In contrast, if X is a discrete metric space with Yu's property (A), then any ideal in Cu*(X) is the closure of the finite propagation operators in the ideal.

AB - Let Cu*(X) be the uniform Roe algebra of a coarse space X with uniformly locally finite coarse structure. We show that an operator G in Cu*(X) is a ghost element if and only if the finite propagation operators in the principal ideal 〈G〉 are all compact operators. In contrast, if X is a discrete metric space with Yu's property (A), then any ideal in Cu*(X) is the closure of the finite propagation operators in the ideal.

UR - https://www.scopus.com/pages/publications/21644487191

U2 - 10.1007/s00013-005-1189-1

DO - 10.1007/s00013-005-1189-1

M3 - 文章

AN - SCOPUS:21644487191

SN - 0003-889X

VL - 84

SP - 519

EP - 526

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 6

ER -

Ghost ideals in uniform Roe algebras of coarse spaces

Abstract

Access to Document

Other files and links

Fingerprint

Cite this