Operator refinements of Schwarz inequality in inner product spaces

Abstract

Some improvements of the celebrated Schwarz inequality in complex inner product spaces in terms of selfadjoint operators $0\le A\le 1_H$ are given. Applications for orthonormal families of vectors are also provided.

Keywords:

• Inner product spaces
• Schwarz’s inequality

AMS Subject Classifications:

• 46C05
• 26D15

Acknowledgements

The author would like to thank the anonymous referees for their valuable comments that have been implemented in the final version of the paper.

Notes

No potential conflict of interest was reported by the author.