The applications of Cauchy-Schwartz inequality for Hilbert modules to elementary operators and i.p.t.i. transformers

Abstract

We apply the inequality $\left|⟨x,y⟩\right|\le \Vert x\Vert {⟨y,y⟩}^{1/2}$ to give an easy and elementary proof of many operator inequalities for elementary operators and inner type product integral transformers obtained during last two decades, which also generalizes all of them.

11 pages