Improved operator Kantorovich and Wielandt inequalities for positive linear maps

TL;DR

This paper enhances and broadens the operator versions of Kantorovich and Wielandt inequalities for positive linear maps on Hilbert spaces, providing more comprehensive and precise results than previous studies.

Contribution

It introduces improved and generalized inequalities for positive linear maps, extending prior work by Fu, He, and Zhang.

Findings

More extensive and precise inequalities established

Generalizations improve upon previous bounds

Results applicable to a wider class of positive linear maps

Abstract

In this paper, we improve and generalize the operator versions of Kantorovich and Wielandt inequalities for positive linear maps on Hilbert space. Our results are more extensive and precise than many previous results due to Fu and He [Linear Multilinear Algebra, doi: 10. 1080/03081087. 2014. 880432.] and Zhang [Banach J. Math. Anal., 9 (2015), no. 1, 166-172.].