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

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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 L1(ℝ), L1(double-struck T sign) and the disc algebra A(double-struck D sign) are not ring homomorphic images of C*-algebras.

Original languageEnglish
Pages (from-to)1789-1794
Number of pages6
JournalProceedings of the American Mathematical Society
Volume124
Issue number6
Publication statusPublished - Dec 1 1996

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Keywords

  • Commutative Banach algebra
  • Gelfand represen-
  • Ring homomorphism

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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