Mappings preserving zero products

Volume 155 / 2003

M. A. Chebotar, W.-F. Ke, P.-H. Lee, N.-C. Wong Studia Mathematica 155 (2003), 77-94 MSC: 08A35, 46L40, 47B48. DOI: 10.4064/sm155-1-6

Abstract

Let $\theta : {{\cal M}}\to {{\cal N}}$ be a zero-product preserving linear map between algebras. We show that under some mild conditions $\theta $ is a product of a central element and an algebra homomorphism. Our result applies to matrix algebras, standard operator algebras, $C^*$-algebras and $W^*$-algebras.

Authors

  • M. A. ChebotarChang Jung Christian University
    Kway Jen
    Tainan 711, Taiwan
    e-mail
  • W.-F. KeDepartment of Mathematics
    National Cheng Kung University
    Tainan 701, Taiwan
    e-mail
  • P.-H. LeeDepartment of Mathematics
    National Taiwan University
    Taipei 106, Taiwan
    e-mail
  • N.-C. WongDepartment of Applied Mathematics
    National Sun Yat-sen University
    Kaohsiung 804, Taiwan
    e-mail

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