Orthogonal forms and orthogonality preservers on real function algebras revisited

2015/11/26 by Antonio M. Peralta, Peralta, Antonio M.
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.1511.08420

arxiv created 2015/11/26 · openalex publication_date 2015/11/26 · arxiv updated 2015/11/30 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In 2014, we determine the precise form of a continuous orthogonal form on a commutative real C^*-algebra. We also describe the general form of a (not-necessarily continuous) orthogonality preserving linear map between commutative unital real C^*-algebras. Among the consequences, we show that every orthogonality preserving linear bijection between commutative unital real C^*-algebras is continuous. In this note we revisit these results and their proofs with the idea of filling a gap in the arguments, and to extend the original conclusions.

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