Zagreb Workshop on Operator Theory

Adjacency preserving maps

Self-adjoint operators represent bounded observables in the mathematical foundations of quantum mechanics. One can define several operations and relations on such operators that are important in mathematical physics. Symmetries are bijective maps acting on the set of all self-adjoint operators preserving one or more such operations and/or relations. We will be interested in the description of the general form of such maps. The connections with geometry will be presented. All the main ideas can be explained in the finite-dimensional case, that is, in the linear algebra setting. We will also discuss related problems on effect algebras.