Zero product preserving maps of operator-valued functions

Wen Fong Ke, Bing Ren Li, Ngai Ching Wong

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

Let X, Y be locally compact Hausdorff spaces and M, N be Banach algebras. Let θ: C0(X, M) → C0(Y, N) be a zero product preserving bounded linear map with dense range. We show that θ is given by a continuous field of algebra homomorphisms from M into N if N is irreducible. As corollaries, such a surjective θ arises from an algebra homomorphism, provided that M is a W*-algebra and N is a semi-simple Banach algebra, or both M and N are C*-algebras.

Original languageEnglish
Pages (from-to)1979-1985
Number of pages7
JournalProceedings of the American Mathematical Society
Volume132
Issue number7
DOIs
Publication statusPublished - 2004 Jul

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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