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.

Keywords:

• Continuous functions
• Birkhoff–James orthogonality
• sesquilinear forms
• Bhatia–Šemrl Theorem

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary 46E10
• Secondary47A07
• 46A32

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).

Additional information

Funding

The research of Mr. Saikat Roy is supported by CSIR MHRD in the form of Junior Research Fellowship.