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Research Article | Open Access

Some zero product preserving additive mappings of operator algebras

Wenbo Huang1,2( ), Jiankui Li2, Shaoze Pan3
School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China
School of Mathematics, East China University of Science and Technology, Shanghai 200237, China
College of Science, Wuxi University, Wuxi 214105, China
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Abstract

Let M be a von Neumann algebra without direct commutative summands, and let A be an arbitrary subalgebra of LS(M) containing M, where LS(M) is the ∗-algebra of all locally measurable operators with respect to M. Suppose δ is an additive mapping from A to LS(M) that satisfies the condition δ(A)B∗+Aδ(B)+δ(B)A∗+Bδ(A)=0 whenever AB=BA=0. In this paper, we prove that there exists an element Y in LS(M) such that δ(X)=XY−YX∗, for every X in A.

Keywords

AF algebraJordan ∗-derivationlocally measurable operatorproperly infinite C∗-algebravon Neumann algebra
CLC number: 46L57, 47B47, 47C15

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 22213-22224
DOI: 10.3934/math.20241080

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Huang W, Li J, Pan S. Some zero product preserving additive mappings of operator algebras. AIMS Mathematics, 2024, 9(8): 22213-22224. https://doi.org/10.3934/math.20241080

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Received: 08 May 2024
Revised: 25 June 2024
Accepted: 03 July 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)