Multiplicative ∗-Jordan type higher derivations on von Neumann algebras. Issue 12 (1st December 2020)

• Record Type: Journal Article
• Authors: Wani, Bilal Ahmad; Ashraf, Mohammad; Lin, Wenhui
• Is Part Of: Quaestiones mathematicae. Volume 43:Issue 12(2020)
• Page Start: 1689
• Page End: 1711
• Publication Date: 2020-12-01
• Subjects: 47B47 -- 16W25 -- 46K15; Multiplicative ∗-Lie n-derivation -- multiplicative ∗-Lie n-higher derivation -- von Neumann algebra; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2019.1649734
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: Let be a von Neumann algebra without nonzero central abelian projections on a complex Hilbert space . Let pn ( X 1, X 2, · · ·, Xn ) be the polynomial defined by n indeterminates X 1, · · ·, Xn and their Jordan multiple ∗-products. In this paper it is shown that a family 𝒟 = { dm } m ∈ℕ of mappings such that, the identity map on satisfies the condition for all U 1, U 2, · · ·, Un ∈ and for each m ∈ ℕ if and only if 𝒟 = { dm } m ∈ℕ is an additive ∗-higher derivation.