Orthogonality of sesquilinear forms and spaces of operators

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.