Communications of the
Korean Mathematical Society CKMS

Let $A$ be a unital Banach algebra and let $\theta: A\longrightarrow A$ be a homomorphism. In this paper, we study linear maps $T: A\longrightarrow A$ which are $\theta$-centralizers at zero or identity products, and under special hypotheses we show that every such linear map is a $\theta$-centralizer. Zero and identity Jordan products preservers, and a more restrictive version of them are also discussed.

Keywords: Centralizer, $\theta$-centralizer, bilinear map, semisimple

MSC numbers: Primary 47B47, 47B49; Secondary 46H25