On C*-algebras associated with C*-correspondences

Takeshi Katsura

doi:10.1016/j.jfa.2004.03.010

On C-algebras associated with C-correspondences

Takeshi Katsura

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

153 Citations (Scopus)

Abstract

We study C*-algebras arising from C* -correspondences, which were introduced by the author. We prove the gauge-invariant uniqueness theorem, and obtain conditions for our C*-algebras to be nuclear, exact, or satisfy the Universal Coefficient Theorem. We also obtain a 6-term exact sequence of K-groups involving the K-groups of our C*-algebras.

Original language	English
Pages (from-to)	366-401
Number of pages	36
Journal	Journal of Functional Analysis
Volume	217
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2004.03.010
Publication status	Published - 2004 Dec 15
Externally published	Yes

Keywords

C*-correspondences
Cuntz-Pimsner algebras
Exact
Gauge action
Hilbert modules
K-groups
Nuclear

ASJC Scopus subject areas

Analysis

Access to Document

10.1016/j.jfa.2004.03.010

Cite this

@article{2317c9d8754942cdbf090ca5b901b13e,

title = "On C*-algebras associated with C*-correspondences",

abstract = "We study C*-algebras arising from C* -correspondences, which were introduced by the author. We prove the gauge-invariant uniqueness theorem, and obtain conditions for our C*-algebras to be nuclear, exact, or satisfy the Universal Coefficient Theorem. We also obtain a 6-term exact sequence of K-groups involving the K-groups of our C*-algebras.",

keywords = "C*-correspondences, Cuntz-Pimsner algebras, Exact, Gauge action, Hilbert modules, K-groups, Nuclear",

author = "Takeshi Katsura",

note = "Funding Information: The author thanks Narutaka Ozawa, who kindly gave Example 7.7 and the proof of Proposition A.13. He is also grateful to N. Christopher Phillips for many comments, and to Yasuyuki Kawahigashi for constant encouragement. This paper was written while the author was staying at University of Oregon. He thanks people there for their warm hospitality. The author was supported in part by a Research Fellowship for Young Scientists of the Japan Society for the Promotion of Science.",

year = "2004",

month = dec,

day = "15",

doi = "10.1016/j.jfa.2004.03.010",

language = "English",

volume = "217",

pages = "366--401",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - On C*-algebras associated with C*-correspondences

AU - Katsura, Takeshi

N1 - Funding Information: The author thanks Narutaka Ozawa, who kindly gave Example 7.7 and the proof of Proposition A.13. He is also grateful to N. Christopher Phillips for many comments, and to Yasuyuki Kawahigashi for constant encouragement. This paper was written while the author was staying at University of Oregon. He thanks people there for their warm hospitality. The author was supported in part by a Research Fellowship for Young Scientists of the Japan Society for the Promotion of Science.

PY - 2004/12/15

Y1 - 2004/12/15

N2 - We study C*-algebras arising from C* -correspondences, which were introduced by the author. We prove the gauge-invariant uniqueness theorem, and obtain conditions for our C*-algebras to be nuclear, exact, or satisfy the Universal Coefficient Theorem. We also obtain a 6-term exact sequence of K-groups involving the K-groups of our C*-algebras.

AB - We study C*-algebras arising from C* -correspondences, which were introduced by the author. We prove the gauge-invariant uniqueness theorem, and obtain conditions for our C*-algebras to be nuclear, exact, or satisfy the Universal Coefficient Theorem. We also obtain a 6-term exact sequence of K-groups involving the K-groups of our C*-algebras.

KW - C-correspondences

KW - Cuntz-Pimsner algebras

KW - Exact

KW - Gauge action

KW - Hilbert modules

KW - K-groups

KW - Nuclear

UR - http://www.scopus.com/inward/record.url?scp=4344667779&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4344667779&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2004.03.010

DO - 10.1016/j.jfa.2004.03.010

M3 - Article

AN - SCOPUS:4344667779

SN - 0022-1236

VL - 217

SP - 366

EP - 401

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -