On the Cauchy-Schwarz inequality and its reverse in semi-inner product \(C^*\)-modules. (English) Zbl 1134.46036

Iliševic, Dijana; Varošanec, Sanja

Banach J. Math. Anal. 1, No. 1, 78-84 (2007).

There are many known Cauchy-Schwarz-type inequalities which are valid in different frameworks. In this paper, we consider the \(A\)-valued Cauchy-Schwarz inequality and its reverse in a semi-inner product \(A\)-module over the \(C^*\)-algebra \(A\). Some remarks on the \(A\)-valued Cauchy-Schwarz inequality in a semi-inner product \(A\)-module over the \(H^*\)-algebra \(A\) are also given.

MSC:

46L08	\(C^*\)-modules
26D07	Inequalities involving other types of functions