Research Article

A characterization of derivations of JSL algebras

Published in: Quaestiones Mathematicae
Volume 46 , issue 12 , 2023 , pages: 2507–2516

DOI: 10.2989/16073606.2023.2169205

Author(s): Lin Chen Changshu Institute of Technology, P.R. China , Jun Li Changshu Institute of Technology, P.R. ChinaChina , Zijie Qin Changshu Institute of Technology, P.R. ChinaChina

Keywords: Primary: 47A30 , Secondary: 47B49 , Jordan derivable mapping , derivation , JSL algebra

Download full text Get new issue alerts

Abstract

Let be a -subspace lattice algebra on a Banach space X and Inv() be the set of all invertible elements of . Suppose that δ : → is a linear mapping satisfying δ(A) ◦ A ⁻¹ + A ◦ δ(A ⁻¹ = 2δ(I) with A ∈ Inv(), where I is the identity element of and ◦ denotes the Jordan product A ◦ B = AB + BA for all A, B ∈ . We show that δ is a derivation. This result can apply to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras. Moreover, we give a characterization of Jordan derivation on Banach algebra with unity by the consideration of a continuous bilinear map.

« Gradient estimates of a nonlinear Lichnerowicz equation under the Finsler-geometric flow

On mixed metric dimension in subdivision, middle, and total graphs »