Best approximations, distance formulas and orthogonality in C*-algebras

2021/01/15 by Priyanka Grover, Sushil Singla, Grover, Priyanka +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA

paper · pdf · doi:10.48550/arxiv.2101.06059

To appear in Journal of the Ramanujan Mathematical Society

arxiv created 2021/01/15 · openalex publication_date 2021/01/15 · arxiv updated 2021/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a unital C^*-algebra \mathcal A and a subspace \mathcal B of \mathcal A, a characterization for a best approximation to an element of \mathcal A in \mathcal B is obtained. As an application, a formula for the distance of an element of \mathcal A from \mathcal B has been obtained, when a best approximation of that element to \mathcal B exists. Further, a characterization for Birkhoff-James orthogonality of an element of a Hilbert C^*-module to a subspace is obtained.

Related

• Distance and best approximations in operator norm and trace class norm
• Numerical radius orthogonality in C^*-algebras
• New estimates for numerical radius in C^*-algebras
• A generalized Birkhoff-James orthogonality and norm parallelism in unital C^*-algebras and their characterizations
• Diameter of the BJ-orthograph in finite dimensional C^*-algebras