### Abstract

For a locally compact group G, every G-invariant subspace E of the Fourier-Stieltjes algebra B(G) gives rise to the following two ideals of the group C^{∗}-algebra C^{∗}(G): the intersection of the kernels of the representations with many coefficient functions in E, and the preannihilator of E. We investigate the question of whether these two ideals coincide. This leads us to define and study two properties of E — ordered and weakly ordered — that measure how many positive definite functions E contains.

Original language | English (US) |
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Pages (from-to) | 1039-1055 |

Number of pages | 17 |

Journal | New York Journal of Mathematics |

Volume | 24 |

State | Published - Oct 23 2018 |

### Fingerprint

### Keywords

- Coaction
- Fourier-stieltjes algebra
- Locally compact group
- Positive definite function

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*New York Journal of Mathematics*,

*24*, 1039-1055.

**Ordered invariant ideals of fourier-stieltjes algebras.** / Kaliszewski, Steven; Landstad, Magnus B.; Quigg, John.

Research output: Contribution to journal › Article

*New York Journal of Mathematics*, vol. 24, pp. 1039-1055.

}

TY - JOUR

T1 - Ordered invariant ideals of fourier-stieltjes algebras

AU - Kaliszewski, Steven

AU - Landstad, Magnus B.

AU - Quigg, John

PY - 2018/10/23

Y1 - 2018/10/23

N2 - For a locally compact group G, every G-invariant subspace E of the Fourier-Stieltjes algebra B(G) gives rise to the following two ideals of the group C∗-algebra C∗(G): the intersection of the kernels of the representations with many coefficient functions in E, and the preannihilator of E. We investigate the question of whether these two ideals coincide. This leads us to define and study two properties of E — ordered and weakly ordered — that measure how many positive definite functions E contains.

AB - For a locally compact group G, every G-invariant subspace E of the Fourier-Stieltjes algebra B(G) gives rise to the following two ideals of the group C∗-algebra C∗(G): the intersection of the kernels of the representations with many coefficient functions in E, and the preannihilator of E. We investigate the question of whether these two ideals coincide. This leads us to define and study two properties of E — ordered and weakly ordered — that measure how many positive definite functions E contains.

KW - Coaction

KW - Fourier-stieltjes algebra

KW - Locally compact group

KW - Positive definite function

UR - http://www.scopus.com/inward/record.url?scp=85056282280&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056282280&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85056282280

VL - 24

SP - 1039

EP - 1055

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

SN - 1076-9803

ER -