Some extensions of Rotfel’d theorem

Abstract

We proved some inequalities for concave functions. Those inequalities complemented a theorem obtained by Lee. Finally, we partially solved an open problem proposed by Zhang P.

Keywords:

• Rotfel’d theorem
• numerical ranges
• concave function
• unitarily invariant norms

AMS Subject Classifications:

• 15A45
• 47A63

Acknowledgements

The authors would like to express their thanks to editor and reviewer(s) for their careful reading and valuable comments and suggestions, which lead a great improvement of this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors’ work was partially supported by the National Natural Science Foundation of China (NSFC) [grant number 11161040].