Characterizations of operator order for k strictly positive operators

Abstract

Abstract. Let A i (i = 1,2,··· ,k) be bounded linear operators on a Hilbert space. This paper aims to show a characterization of operator order A k A k−1 ··· A 2 A 1 > 0 in terms of operator inequalities. Afterwards, an application of the characterization is given to operator equalities due to Douglas's majorization and factorization theorem. Mathematics subject classification