Some Grüss Type Inequalities for Fréchet Differentiable Mappings

T. Teimouri-Azadbakht ; A. G Ghazanfari

Kragujevac Journal of Mathematics, Tome 44 (2020) no. 4, p. 571 .

Résumé

Let $X$ be a Hilbert $C^{*}$-module on $C^{*}$-algebra $A$ and $p\in A$. We denote by $D_{p}(A ,X)$ the set of all continuous functions $f : A \rightarrow X$, which are Fréchet differentiable on a open neighborhood $U$ of $p$. Then, we introduce some generalized semi-inner products on $D_{p}(A ,X)$, and using them some Grüss type inequalities in semi-inner product $C^*$-module $D_{p}(A ,X)$ and $D_{p}(A ,X^n)$ are established.

Détail

Classification : 26D10 46C05, 46L08
Keywords: Fréchet differentiable mappings, $C^*$-modules, Grüss inequality