## Zero product preserving maps of operator-valued functions

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- by Wen-Fong Ke, Bing-Ren Li and Ngai-Ching Wong PDF
- Proc. Amer. Math. Soc.
**132**(2004), 1979-1985 Request permission

## Abstract:

Let $X,Y$ be locally compact Hausdorff spaces and ${\mathcal M}$, ${\mathcal N}$ be Banach algebras. Let $\theta : C_0(X,{\mathcal M}) \to C_0(Y, {\mathcal N})$ be a zero product preserving bounded linear map with dense range. We show that $\theta$ is given by a continuous field of algebra homomorphisms from ${\mathcal M}$ into ${\mathcal N}$ if ${\mathcal N}$ is irreducible. As corollaries, such a surjective $\theta$ arises from an algebra homomorphism, provided that ${\mathcal M}$ is a $W^*$-algebra and ${\mathcal N}$ is a semi-simple Banach algebra, or both ${\mathcal M}$ and ${\mathcal N}$ are $C^*$-algebras.## References

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## Additional Information

**Wen-Fong Ke**- Affiliation: Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan
- Email: wfke@mail.ncku.edu.tw
**Bing-Ren Li**- Affiliation: Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, China
- Email: brli@mail2.math.ac.cn
**Ngai-Ching Wong**- Affiliation: Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan
- Email: wong@math.nsysu.edu.tw
- Received by editor(s): July 25, 2002
- Received by editor(s) in revised form: March 7, 2003
- Published electronically: December 15, 2003
- Communicated by: David R. Larson
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**132**(2004), 1979-1985 - MSC (2000): Primary 46E40, 47B33
- DOI: https://doi.org/10.1090/S0002-9939-03-07321-0
- MathSciNet review: 2053969