Abstract
In this paper we introduce the concept of quadratic operator perspective for a continuous function defined on the positive semi-axis of real numbers, the invertible operator and operator on a Hilbert space by
This generalize the quadratic weighted operator geometric mean of defined by
for and the quadratic relative operator entropy defined by
Some inequalities for this perspective of convex functions are established. Applications for quadratic weighted operator geometric mean and quadratic relative operator entropy are also provided.
Acknowledgement
The author would like to thank the anonymous referee for valuable suggestions that have been implemented in the final version of the manuscript.
Citation
S.S. Dragomir. "Inequalities for quadratic operator perspective of convex functions and bounded linear operators on Hilbert spaces." SUT J. Math. 53 (1) 39 - 58, June 2017. https://doi.org/10.55937/sut/1505482247
Information