Maps preserving two-sided zero products on zero product determined Banach algebras

Seminario de Jóvenes Investigadores

Speaker: Marisa C. Godoy, Universidad de Granada

Abstract: Let A and B be Banach algebras and let Φ: A → B be a surjective continuous linear map which preserves two-sided zero products (i.e., Φ(a)Φ(b) = Φ(b)Φ(a) = 0 whenever ab = ba = 0). We show that Φ is a weighted Jordan homomorphism provided that A is zero product determined, is weakly amenable and admits a bounded approximate identity. These conditions are in particular fulfilled when A is the group algebra L¹(G) with G any locally compact group or a C*-algebra.

Where: Seminario 2