Characterizing Jordan maps through products at a fixed element

Start: 19 June 2026 10:00
End: 19 June 2026 11:00
Categories: Conference , Seminar , Instituto de Matemáticas UGR

Where: Seminario Departamento de Análisis Matemático, Facultad de Ciencias

IMAG Functional Analysis Seminar
Title: Characterizing Jordan maps through products at a fixed element
By Jorge J. Garcés (UNED)
Abstract: We shall present some new and old results on linear maps that (in some sense) behave as a Jordan homomorphism or a Jordan derivation locally. More generally, by paralleling the theory of Jordan zero-product determined algebras, we study von Neumann algebras that are square-zero determined or determined by Jordan products at a fixed point and show that all properly infinite von Neumann factors are both square-zero determined and determined by Jordan zero-products at any fixed point. Finally, we shall discuss a generalisation of these results to more general classes of von Neumann algebras.Part of the results of this talk are from a joint work with Mykola Khrypchenko https://doi.org/10.1016/j.laa.2025.09.013