Roberts numerical radius orthogonality

ABSTRACT

We deal with the Roberts numerical radius orthogonality. In the case of 2 × 2 complex matrices, we give some necessary and sufficient conditions for the numerical range to be symmetric by employing the Roberts orthogonality with respect to the numerical radius. In addition, we present an interrelation between the Roberts orthogonality and the Birkhoff–James orthogonality with respect to the numerical radius for n × n complex matrices. Some other related results are also discussed.

Keywords:

• Roberts orthogonality
• Birkhoff–James orthogonality
• numerical range
• numerical radius

2010 Mathematics Subject Classifications:

• Primary 47A12
• Secondary 15A60
• 47L05

Acknowledgments

The authors would like to thank the referee for several valuable suggestions and comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).