Preservers

The main topic of our research project is the generalization of linear preserver problems to problems for preservers, which are not necessarily linear. We will try to find reasonable and as weak assumptions as possible, which will still assure similar characterization of preservers as in the linear case. First, we will try to generalize the Frobenius result about linear mappings, which leave the determinant invariant, to mappings which are not necessarily linear and preserve the determinant. Further on, we will work on the generalization of some other classical linear preserver problems, such as rank, spectrum, commutativity preservers... One of the primary aims of the research will be replacing the assumption of linearity with as weak and as unified assumptions as possible.