Advances in Operator Cauchy--Schwarz inequalities and their reverses

• DOI: 10.15352/afa/06-3-20
• Publication Date: 2015-07-16T20:33:34Z
• Authors: J. M. Aldaz; S. Barza; M. Fujii; M. S. Moslehian
• Keywords: Cauchy–Schwarz inequality; Operator (biology); Ky Fan inequality

The Cauchy-Schwarz (C-S) inequality is one of the most famous inequalities in mathematics. In this survey article, we first give a brief history of the inequality. Afterward, we present the C-S inequality for inner product spaces. Focusing on operator inequalities, we then review some significant recent developments of the C-S inequality and its reverses for Hilbert space operators and elements of Hilbert C*-modules. In particular, we pay special attention to an operator Wielandt inequality.