Linear preserver problems: A brief introduction and some special techniques

AbstractLinear preserver problems concern the characterization of linear operators on matrix spaces that leave certain functions, subsets, relations, etc., invariant. The earliest papers on linear preserver problems date back to 1897, and a great deal of effort has been devoted to the study of this type of question since then. We present a brief picture of the subject, aiming at giving a gentle introduction to the reader. Then we describe some techniques used in our recent papers on this type of problem