Operator upper bounds for Davis-Choi-Jensen’s difference in Hilbert spaces
Mathematica Moravica, Tome 28 (2024) no. 1.
Voir la notice de l'article dans eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
In this paper we obtain several operator inequalities providing upper bounds for the Davis-Choi-Jensen's Difference
$\Phi ((A)) - (\Phi(A))$ for any convex function $f:I\rightarrow \mathbb{R}$, any selfadjoint operator $A$ in $H$ with the spectrum $\limfunc{Sp}\left( A\right) \subset I$ and any linear, positive and normalized map $\Phi :\mathcal{B}\left(H\right) \rightarrow \mathcal{B}\left(K\right)$, where $H$ and $K$ are Hilbert spaces. Some examples of convex and operator convex functions are also provided.
Mots-clés :
Selfadjoint bounded linear operators, Functions of operators, Operator convex functions, Jensen’s operator inequality, Linear, positive and normalized map.
@article{MM3_2024_28_1_a3,
author = {Silvestru Sever Dragomir},
title = {Operator upper bounds for {Davis-Choi-Jensen{\textquoteright}s} difference in {Hilbert} spaces},
journal = {Mathematica Moravica},
pages = {39 - 51},
publisher = {mathdoc},
volume = {28},
number = {1},
year = {2024},
url = {https://geodesic-test.mathdoc.fr/item/MM3_2024_28_1_a3/}
}
Silvestru Sever Dragomir. Operator upper bounds for Davis-Choi-Jensen’s difference in Hilbert spaces. Mathematica Moravica, Tome 28 (2024) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2024_28_1_a3/