Gruss type inequalities in semi-inner product C*-modules and applications

TL;DR

This paper establishes Gruss type inequalities within semi-inner product modules over C*-algebras and explores their applications in approximating Fourier and Melin transforms of bounded operators.

Contribution

It introduces new Gruss inequalities in semi-inner product C*-modules and applies them to operator transform approximations.

Findings

New Gruss inequalities for semi-inner product modules over C*-algebras

Applications to approximation of Fourier transforms of operators

Applications to approximation of Melin transforms of operators

Abstract

Some Gruss type inequalities in semi-inner product modules over C*-algebras for n-tuples of vectors are established. Also we give their natu- ral applications for the approximation of the discrete Fourier and the Melin transforms of bounded linear operators on a Hilbert space.