Characterization of n-Jordan multipliers of Banach algebras

CHARACTERIZATION OF n-JORDAN MULTIPLIERS OF BANACH ALGEBRAS Akçay B. Aydın Adnan Menderes University, Graduate School of Natural and Applied Sciences, Department of Mathematics, Master Thesis, Supervisor: Asst. Prof. Berna Arslan, Aydın, 2024. Objective: In this thesis, it is aimed to compile some of the properties obtained in the studies on n-Jordan multipliers defined on Banach algebras so far and to bring together the basic information about the subject in case of a study in this field. Material and Methods: While preparing this thesis, which is purely theoretical, previous studies on n-Jordan multipliers were examined and internet resources were utilized. Results: We study n-Jordan multipliers in Banach algebras, present examples of this notion, characterize it by its action on the zero product, and study the properties it provides in C ∗ -algebras and in the group algebra L 1 (G) of a commutative locally compact group G. Conclusion: Studying characterizations on various spaces, such as the group algebra L 1 (G) of a locally compact group G, unital Banach algebras generated by idempotents, or C ∗ -algebras, will help to better understand the structure of multipliers and Jordan multipliers defined in Banach algebras. New examples of algebraic structures can be obtained to make similar characterizations. Furthermore, the implications of the known knowledge on types of derivations in Banach algebras for n-multipliers and n-Jordan multipliers can be investigated. Keywords: Banach algebra, n-Jordan multiplier, property B, amenability, group algebra, C ∗ -algebra.