### Abstract

We prove that if a commutative semi-simple Banach algebra A is the range of a ring homomorphism from a commutative C*-algebra, then A is C*-equivalent, i.e. there are a commutative C*-algebra B and a bicontinuous algebra isomorphism between A and B. In particular, it is shown that the group algebras L^{1}(ℝ), L^{1}(double-struck T sign) and the disc algebra A(double-struck D sign) are not ring homomorphic images of C*-algebras.

Original language | English |
---|---|

Pages (from-to) | 1789-1794 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 124 |

Issue number | 6 |

Publication status | Published - 1996 |

### Fingerprint

### Keywords

- Commutative Banach algebra
- Gelfand represen-
- Ring homomorphism

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*124*(6), 1789-1794.

**The range of a ring homomorphism from a commutative C*-algebra.** / Molnár, L.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 124, no. 6, pp. 1789-1794.

}

TY - JOUR

T1 - The range of a ring homomorphism from a commutative C*-algebra

AU - Molnár, L.

PY - 1996

Y1 - 1996

N2 - We prove that if a commutative semi-simple Banach algebra A is the range of a ring homomorphism from a commutative C*-algebra, then A is C*-equivalent, i.e. there are a commutative C*-algebra B and a bicontinuous algebra isomorphism between A and B. In particular, it is shown that the group algebras L1(ℝ), L1(double-struck T sign) and the disc algebra A(double-struck D sign) are not ring homomorphic images of C*-algebras.

AB - We prove that if a commutative semi-simple Banach algebra A is the range of a ring homomorphism from a commutative C*-algebra, then A is C*-equivalent, i.e. there are a commutative C*-algebra B and a bicontinuous algebra isomorphism between A and B. In particular, it is shown that the group algebras L1(ℝ), L1(double-struck T sign) and the disc algebra A(double-struck D sign) are not ring homomorphic images of C*-algebras.

KW - Commutative Banach algebra

KW - Gelfand represen-

KW - Ring homomorphism

UR - http://www.scopus.com/inward/record.url?scp=21344463037&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344463037&partnerID=8YFLogxK

M3 - Article

VL - 124

SP - 1789

EP - 1794

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 6

ER -