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2-local automorphisms of arens algebras.
- Source :
- AIP Conference Proceedings; 2024, Vol. 3147 Issue 1, p1-6, 6p
- Publication Year :
- 2024
-
Abstract
- The focus of this paper is to examine 2-local automorphisms of the Arens algebra L<superscript>ω</superscript> (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 L<superscript>p</superscript> (M,τ) is a Banach space defined L<superscript>p</superscript> (M,τ)={x ∈ S(M,τ) :τ (| x |<superscript>p</superscript>)<∞} for p≥1. We will show that the surjective 2-local involutive automorphism Φ of the Arens algebra L<superscript>ω</superscript> (M,τ) identically acting on the center is an inner automorphism, i.e. there is a unitary element u of the Arens algebra L<superscript>ω</superscript> (M,τ) such that Φ(x)=uxu* for all x ∈ L<superscript>ω</superscript> (M,τ). It is required that the automorphism ϕ<subscript>x, y</subscript> (x) for an arbitrary pair (x, y), satisfying the conditions ϕ<subscript>x, y</subscript> (x)=Φ(x) and ϕ<subscript>x, y</subscript> (y)=Φ(y), acts identically on the center of the Arens algebra. [ABSTRACT FROM AUTHOR]
- Subjects :
- VON Neumann algebras
AUTOMORPHISMS
NONCOMMUTATIVE algebras
ALGEBRA
BANACH spaces
Subjects
Details
- Language :
- English
- ISSN :
- 0094243X
- Volume :
- 3147
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- AIP Conference Proceedings
- Publication Type :
- Conference
- Accession number :
- 177065343
- Full Text :
- https://doi.org/10.1063/5.0210130