### Abstract

Huruya [4] has proven that, for C*-algebras A_{1}and A_{2}(A_{1}⊗ A_{2})** = A_{1}**⊗ A_{2}** for every A_{2}if and only if A_{1}is scattered. We strengthen this by proving that (A_{1}⊗ A_{2})** = A_{1}**⊗ A_{2}** if and only if A_{1}or A_{2}is scattered. We discuss ramifications to representation theory and related questions regarding normal representations of W*-tensor products.

Original language | English (US) |
---|---|

Pages (from-to) | 666-668 |

Number of pages | 3 |

Journal | Proceedings of the American Mathematical Society |

Volume | 100 |

Issue number | 4 |

DOIs | |

State | Published - 1987 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**On biduals of C*-tensor products.** / Quigg, John.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 100, no. 4, pp. 666-668. https://doi.org/10.1090/S0002-9939-1987-0894435-4

}

TY - JOUR

T1 - On biduals of C*-tensor products

AU - Quigg, John

PY - 1987

Y1 - 1987

N2 - Huruya [4] has proven that, for C*-algebras A1and A2(A1⊗ A2)** = A1**⊗ A2** for every A2if and only if A1is scattered. We strengthen this by proving that (A1⊗ A2)** = A1**⊗ A2** if and only if A1or A2is scattered. We discuss ramifications to representation theory and related questions regarding normal representations of W*-tensor products.

AB - Huruya [4] has proven that, for C*-algebras A1and A2(A1⊗ A2)** = A1**⊗ A2** for every A2if and only if A1is scattered. We strengthen this by proving that (A1⊗ A2)** = A1**⊗ A2** if and only if A1or A2is scattered. We discuss ramifications to representation theory and related questions regarding normal representations of W*-tensor products.

UR - http://www.scopus.com/inward/record.url?scp=84968503774&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968503774&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1987-0894435-4

DO - 10.1090/S0002-9939-1987-0894435-4

M3 - Article

AN - SCOPUS:84968503774

VL - 100

SP - 666

EP - 668

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -