The theory of functional identities has been developed in the last 15 years and this is the first book devoted exclusively to this topic. The theory of functional identities was initiated by M. Brešar in the beginning of the 90’s. A number of mathematicians have contributed to the creation of the theory, especially K. I. Beidar and coauthors of the book M. A. Chebotar and W. S. Martindale. The book is written for researchers and postgraduate students.
COBISS.SI-ID: 14332505
In certain rings containing non-trivial idempotents we consider maps, which are determined by their actions on elements with the zero product. Obtained results are generalizations of some known results about maps preserving the zero product. The most important thing in the article is the discovery of the connections between these maps and the theory of local maps. As an application, we prove that in a prime ring containing a non-trivial idempotent every local derivation is a derivation.
COBISS.SI-ID: 14931289
There are many results published in the literature about characterization of bijective linear maps on algebras, which preserve commutativity. Without assuming bijectivity the problem becomes much harder. We prove that for the finite-dimensional central simple algebra every (not necessarily bijective) commutativity preserving linear map is either of the standard form, or its image is a subset of the center of the algebra.
COBISS.SI-ID: 13984857
Description of maps on idempotent matrices over division rings that preserve either commutativity, or order, or orthogonality is given. The results are as general as possible, that is we consider maps which preserve relation in one direction only, we try to avoid the assumptions of injectivity or surjectivity. We give examples showing that our assumptions cannot be relaxed much further.
COBISS.SI-ID: 13948761
Certain maps are always weak*-continuous on dual spaces If a Banach module over a C*-algebra is a dual Banach space and can be isometrically represented as an operator module, than the action of all elements from the algebra on the module is automatically weak*-continuous. The same is true also for the operator modules over the general operator algebras under the stronger condition, that modules are dual operator spaces.
COBISS.SI-ID: 13633113