2013/09/16 by Jorge J. Garcés, Garcés, Jorge J., Antonio M. Peralta +1
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.1309.3839
To appear in Linear and Multilinear Algebra
arxiv created 2013/09/16 · openalex publication_date 2013/09/16 · arxiv updated 2013/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We initiate the study of orthogonal forms on a real C^*-algebra. Motivated by previous contributions, due to Ylinen, Jajte, Paszkiewicz and Goldstein, we prove that for every continuous orthogonal form V on a commutative real C^*-algebra, A, there exist functionals φ1 and φ2 in A* satisfying V(x,y) = φ1 (x y) + φ2 (x y^*), for every x,y in A. We describe the general form of a (not-necessarily continuous) orthogonality preserving linear map between unital commutative real C^*-algebras. As a consequence, we show that every orthogonality preserving linear bijection between unital commutative real C^*-algebras is continuous.