Grüss type inequalities for positive linear maps and Hilbert $C^{*}$-modules

In this paper, we study some Grüss type inequalities for positive linear maps between $C^{*}$-algebras and for accretive operators. In addition we generalize some Grüss type inequalities for Hilbert $C^{*}$-modules, as well as some classes of adjointable operators on these spaces. We then extend our work to give a Grüss .type inequality for positive linear maps from L(X) into a $C^{*}$-algebra A, where X is a Hilbert A-module