2-local (\upvarphi, \uppsi) -Derivations on Finite von Neumann Algebras

2018/12/09 by Fard, Meysam Habibzadeh
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1812.03430

Abstract

In this paper, I introduce the concept of (\upvarphi, \uppsi) -finite von Neumann algebras and I show that if \mathscrM is a finite and (\upvarphi, \uppsi) -finite von Neumann algebra togather with condition \ ( Δ(u+v)-Δ(u)-Δ(v))^*\ ⊆ \uppsi(\mathscrM) , then each (approximately) 2-local (\upvarphi, \uppsi) -derivation δ on \mathscrM , is a (\upvarphi, \uppsi) -derivation.

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