Weak 2-Local Inner Derivations of Semiprime ∗-Banach Algebras

Boxian Li and Xiangqi Qiang ()
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Boxian Li: School of Science, Jiangsu University of Science and Technology, Zhenjiang 212100, China
Xiangqi Qiang: School of Science, Jiangsu University of Science and Technology, Zhenjiang 212100, China

Mathematics, 2025, vol. 13, issue 22, 1-13

Abstract: This paper introduces and examines the concept of weak 2-local inner derivations and their relationship to P -2-local mappings. It is established that every such mapping on a semiprime ∗-Banach algebra with a faithful trace is a derivation, which also provides a complete characterization on finite von Neumann algebras. Additionally, it is shown that weak 2-local inner derivations coincide with the 2-local reflection closure of the inner derivations.

Keywords: 2-reflexive; weak 2-local inner derivations; semiprime ∗-Banach algebras; finite von Neumann algebras (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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