A note on reverses of the young type inequalities via Kantorovich constant

Abstract

In present paper, we give some new reverses of the Young type inequalities which were established by X. Hu and J. Xue [7] via Kantorovich constant. Then we apply these inequalities to establish corresponding inequalities for the Hilbert-Schmidt norm and the trace norm.

Generalized Kantorovich Constant, a New Formulation and Properties

“…Also, the Kantorovich constant plays a vital role in various improvements of the Young inequality and its reverse for the scalar case, as well as for matrix versions, see [10], [12], [14], [15].…”