Multiplicative ∗-Jordan type higher derivations on von Neumann algebras

Abstract

Let be a von Neumann algebra without nonzero central abelian projections on a complex Hilbert space . Let p_n(X₁, X₂, · · ·, X_n) be the polynomial defined by n indeterminates X₁, · · ·, X_n and their Jordan multiple ∗-products. In this paper it is shown that a family 𝒟 = {d_m}_m∈ℕ of mappings such that , the identity map on satisfies the condition

for all U₁, U₂, · · ·, U_n ∈ and for each m ∈ ℕ if and only if 𝒟 = {d_m}_m∈ℕ is an additive ∗-higher derivation.

Mathematics Subject Classification (2010):

• 47B47
• 16W25
• 46K15

Key words:

• Multiplicative ∗-Lie n-derivation
• multiplicative ∗-Lie n-higher derivation
• von Neumann algebra