Equivalence on some Rotfel’d type theorems

Abstract

In this paper, we prove that some recent Rotfel’d theorem extensions are equivalent.

Keywords:

• Rotfel’d theorem
• concave function
• numerical range
• unitarily invariant norm

AMS Subject Classifications:

• 47A63
• 15A45
• 47A30

Acknowledgements

The authors would like to thank an anonymous referee for his or her valuable suggestions that improved the presentation of this article. Comments from Professor Fuzhen Zhang are also gratefully acknowledged.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by the National Natural Science Foundation of China [grant number 11571220]; the Natural Sciences and Engineering Research Council of Canada (NSERC) [RGPIN 312386-2015].