A Gruss type inequality for vector-valued functions in Hilbert C*-modules

TL;DR

This paper extends the Gruss integral inequality to vector-valued functions within Hilbert C*-modules, providing new theoretical bounds and potential applications in operator algebra contexts.

Contribution

It introduces a novel version of the Gruss inequality specifically for functions valued in Hilbert C*-modules, expanding the scope of classical inequalities.

Findings

Established a new Gruss inequality for Hilbert C*-module valued functions.

Provided applications demonstrating the inequality's utility.

Enhanced understanding of integral inequalities in operator algebra settings.

Abstract

In this paper we prove a version of Gruss integral inequality for mappings with values in Hilbert C*-modules. Some applications for such functions are also given.