Interpolating inequalities related to a recent result of Audenaert

Abstract

Audenaert recently obtained an inequality for unitarily invariant norms that interpolates between the arithmetic–geometric mean inequality and the Cauchy–Schwarz inequality for matrices. A refined version of Audenaert’s inequality for the Hilbert–Schmidt norm is given. Other interpolating inequalities for unitarily invariant norms are also presented.

Keywords:

• Singular value
• Hilbert–Schmidt norm
• unitarily invariant norm
• inequality

AMS Subject Classifications:

• Primary: 15A18
• Secondary: 15A60
• 47A30

Acknowledgements

The authors are grateful to the referee for his comments.

Notes

No potential conflict of interest was reported by the authors.