2018/11/17 by Ali Zamani, Zamani, Ali
Mathematics · #39B55 #46L05 #47B49 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1811.07148
openalex publication_date 2018/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the representation of the so-called orthogonally a-Jensen mappings acting on C^*-modules. More precisely, let \mathfrakA be a unital C^*-algebra with the unit 1, let a ∈ \mathfrakA be fixed such that a, 1-a are invertible and let \mathscrE, \mathscrF, \mathscrG be inner product \mathfrakA-modules. We prove that if there exist additive mappings φ, ψ from \mathscrF into \mathscrE such that ⟨ φ(y), ψ(z)⟩=0 and a ⟨ φ(y), φ(z)⟩ a^∗ = (1 - a)⟨ ψ(y), ψ(z)⟩ (1 - a)^∗ for all y, z∈ \mathscrF, then a mapping f: \mathscrE → \mathscrG is orthogonally a-Jensen if and only if it is of the form f(x) = A(x) + B(x, x) +f(0) for x∈ \mathscrK := φ(\mathscrF)+ψ(\mathscrF), where A: \mathscrE → \mathscrG is an a-additive mapping on \mathscrK and B is a symmetric a-biadditive orthogonality preserving mapping on \mathscrK× \mathscrK. Some other related results are also presented.