φJ-multipliers and φJ-multipliers quadratic on Jordan Banach algebras

In this work, we define the notion of φJ-multipliers on Jordan-Banach algebras without order and investigate some of their properties. We show that a φJ-multiplier satisfies the condition T [Ux(y)] = Uφ(x)[T(y)]. This suggests that we define a new concept which is the φJ-multiplier quadratic. We show several algebraic or topological properties for both concepts. In particular, we extend some known results for φ-multipliers to φJ-multipliers and φJ-multipliers quadratic. © 2014, Forum-Editrice Universitaria Udinese SRL. All rights reserved.