Abstract. We extend some inequalities for normal matrices and positive linear maps related to the Russo-Dye theorem. The results cover the case of some positive linear maps $\Phi $ on a von Neumann algebra ${\mathcal {M}}$ such that $\Phi (X)$ is unbounded for all nonzero $X\in {\mathcal {M}}$.

DOI: 10.14232/actasm-020-671-1

AMS Subject Classification (1991): 47A63, 46L52

Keyword(s): positive linear maps, operator inequalities, $\tau $-measurable operators

received 21.4.2020, revised 6.1.2021, accepted 13.1.2021. (Registered under 421/2020.)