Orthogonality of sesquilinear forms and spaces of operators. Issue 19 (16th December 2022)

• Record Type: Journal Article
• Authors: Roy, Saikat; Bagchi, Satya
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 19(2022)
• Page Start: 4416
• Page End: 4424
• Publication Date: 2022-12-16
• Subjects: Continuous functions -- Birkhoff–James orthogonality -- sesquilinear forms -- Bhatia–Šemrl Theorem; Primary 46E10 -- Secondary47A07 -- 46A32; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.1881034
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : We obtain a necessary and sufficient condition for Birkhoff–James orthogonality in the space of all continuous vector-valued functions from a compact topological space to a finite-dimensional Hilbert space, by using some basic geometric ideas. We apply our outcomes to characterize Birkhoff–James orthogonality of sesquilinear forms. Moreover, using Birkhoff–James orthogonality of sesquilinear forms, we obtain a different proof of the renowned Bhatia–Šemrl Theorem.