Characterizations of operator order for k strictly positive operators

Jian Shi; Zongsheng Gao

paper

Characterizations of operator order for k strictly positive operators

arXiv:1111.3759

Abstract

Let $A_{i} (i = 1, 2, ..., k)$ be bounded linear operators on a Hilbert space. This paper aims to show characterizations of operator order $A_{k} \geq A_{k - 1} \geq ... \geq A_{2} \geq A_{1} > 0$ in terms of operator inequalities. Afterwards, an application of the characterizations is given to operator equalities due to Douglas's majorization and factorization theorem.