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.
2020 MATHEMATICS SUBJECT CLASSIFICATIONS:
Acknowledgments
The authors would like to thank the reviewers for their thoughtful comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).