Geodesic
Mappings preserving zero products
M. A. Chebotar1 ; W.-F. Ke2 ; P.-H. Lee3 ; N.-C. Wong4
1Chang Jung Christian University Kway Jen Tainan 711, Taiwan
2Department of Mathematics National Cheng Kung University Tainan 701, Taiwan
3Department of Mathematics National Taiwan University Taipei 106, Taiwan
4Department of Applied Mathematics National Sun Yat-sen University Kaohsiung 804, Taiwan
Studia Mathematica, Tome 155 (2003) no. 1, pp. 77-94
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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.
DOI : 10.4064/sm155-1-6
Keywords: theta cal cal zero product preserving linear map between algebras under mild conditions theta product central element algebra homomorphism result applies matrix algebras standard operator algebras * algebras * algebras

M. A. Chebotar  1   ; W.-F. Ke  2   ; P.-H. Lee  3   ; N.-C. Wong  4

1 Chang Jung Christian University Kway Jen Tainan 711, Taiwan
2 Department of Mathematics National Cheng Kung University Tainan 701, Taiwan
3 Department of Mathematics National Taiwan University Taipei 106, Taiwan
4 Department of Applied Mathematics National Sun Yat-sen University Kaohsiung 804, Taiwan 
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M. A. Chebotar; W.-F. Ke; P.-H. Lee; N.-C. Wong. Mappings preserving zero products. Studia Mathematica, Tome 155 (2003) no. 1, pp. 77-94. doi: 10.4064/sm155-1-6

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