Semi-centralizing maps of generalized matrix algebras

Centralizing traces and Lie triple isomorphisms on triangular algebras

“…When we investigate the above-mentioned mappings, the principal task is to describe their forms. This is demonstrated by various works, see [8,10,11,12,13,15,20,21,28,29,33,36,41,44,45,49,50]. We encourage the reader to read the well-written survey paper [13], in which the author presented the development of the theory of semi-centralizing mappings and their applications in details.…”

“…Since these examples have already been presented in many papers, we just state their titles without any introduction. We refer the reader to [8,29,49] for more details. …”

“…The distinguished feature of our systematic work is that we deal all questions related to (non-)linear mappings of triangular algebras and full matrix algebras under a unified frame, which is the admired generalized matrix algebras frame, see [25,29,30,47,49,50].…”

Centralizing traces and Lie triple isomorphisms on generalized matrix algebras

“…Let M n (R) be the full matrix algebra consisting of all n × n matrices over R. It is worth to point out that the notion of generalized matrix algebras efficiently unifies triangular algebras with full matrix algebras together. The feature of our systematic work is to deal with all questions related to (non-)linear mappings of triangular algebras and of full matrix algebras under a unified frame, which is the admired generalized matrix algebras frame, see [41,52,53,54,74,75]. Let us list some classical examples of generalized matrix algebras which will be revisited in the sequel (Section 3 and Section 4).…”

“…It was Krylov who initiated the study of linear mappings on generalized matrix algebras from the point of classifying view [47]. Since then many articles are devoted to this topic, and a number of interesting results are obtained (see [12,15,37,38,52,53,54,67,74,75]). Nevertheless, it leaves so much to be desired.…”