Operator inequalities associated with AlogA via Specht ratio

An operator means a bounded linear operator on a Hilbert space H. We obtained the basic property between Specht ratio S(1) and generalized Kantorovich constant K(p) in [Math. Inequal. Appl., in press], that is, Specht ratio S(1) can be expressed by generalized Kantorovich constant K(p): S(1)=eK′(1). We shall investigate several product type and difference type inequalities associated with AlogA by applying this basic property to several Kantorovich type inequalities.