Some general techniques on linear preserver problems

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. (C) 2000 Elsevier Science Inc. All rights reserved.