Search

The focus of this paper is to examine 2-local automorphisms of the Arens algebra Lω (M,τ)) that is connected to a von Neumann algebra. Consider a von Neumann algebra M of type I accompanied by a trustworthy, regular, and semi-finite trace τ, we consider the noncommutative Arens algebra L ω (M , τ) = ∩ p ≥ 1 L p (M , τ) , where Lp (M,τ) is a Banach space defined Lp (M,τ)={x ∈ S(M,τ) :τ (| x |p)<∞} for p≥1. We will show that the surjective 2-local involutive automorphism Φ of the Arens algebra Lω (M,τ) identically acting on the center is an inner automorphism, i.e. there is a unitary element u of the Arens algebra Lω (M,τ) such that Φ(x)=uxu* for all x ∈ Lω (M,τ). It is required that the automorphism ϕx, y (x) for an arbitrary pair (x, y), satisfying the conditions ϕx, y (x)=Φ(x) and ϕx, y (y)=Φ(y), acts identically on the center of the Arens algebra. [ABSTRACT FROM AUTHOR]