## Abstract

Several general techniques on linear preserver problems are described. The first one is based on a transfer principle in Model Theoretic Algebra that allows one to extend linear preserver results on complex matrices to matrices over other algebraically closed fields of characteristic 0. The second one concerns the use of some simple geometric technique to reduce linear preserver problems to standard types so that known results can be applied. The third one is about solving linear preserver problems on more general (operator) algebras by reducing the problems to idempotent preservers. Numerous examples will be given to demonstrate the proposed techniques.

Original language | English |
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Pages (from-to) | 61-81 |

Number of pages | 21 |

Journal | Linear Algebra and Its Applications |

Volume | 315 |

Issue number | 1-3 |

DOIs | |

State | Published - 15 Aug 2000 |

Externally published | Yes |

### Bibliographical note

Funding Information:The first author was supported by RFBR grants NN 96-15-96050, 99-01-00382, the second author by an NSF grant of USA and the third author by a grant from the Ministry of Science of Slovenia. This research started when the authors visited the University of Coimbra after the LPP99 workshop at the University of Lisbon in January 1999. They would like to thank the organizers of the workshop for their support and the colleagues of the two universities for their warm hospitality. Furthermore, they would like to thank Professor Sá for drawing their attention to theory of the transfer principle.

## Keywords

- 15A04
- 47B49
- Algebraically closed fields
- Idempotent
- Linear preserver
- Matrices
- Nilpotent