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Functional identities and their applications
Preview AbstractThis paper surveys the theory of functional identities and its applications. No prior knowledge of the theory is required to follow the paper.
A survey on linear (additive) preserver problems
Preview AbstractThis survey is articulated around two major axis. The first one concerns the Kaplansky problem; the history of the problem and several results are presented. The second one concerns some new preserver problems (concerning the generalized inverse, Fredholm or semi-Fredholm operators). The common point of these results is that they are interesting only in the infinite dimensional situation. Several open questions are mentioned over all the paper.