On operator order and chaotic operator order for two operators Original Research Article

In this paper we characterize operator order Agreater-or-equal, slantedBgreater-or-equal, slantedO and chaotic operator order log Agreater-or-equal, slantedlogB for positive and invertible operators A and B in terms of operator inequalities via the Furuta inequality and operator equalities due to the Douglas’s majorization and factorization. Related results are obtained, which include generalizations and characterizations of some well-known results.