Some Gr\"{u}ss type inequalities for $n$-tuples of vectors in semi-inner modules

TL;DR

This paper establishes Grüss-type inequalities for n-tuples of vectors in semi-inner product modules over C*- and H*-algebras, with applications to approximating Fourier and Melin transforms in these modules.

Contribution

It introduces new Grüss-type inequalities in semi-inner product modules over C*- and H*-algebras, extending previous results to n-tuples of vectors.

Findings

Derived Grüss inequalities for n-tuples of vectors in semi-inner modules.

Applied inequalities to approximate Fourier and Melin transforms.

Extended classical inequalities to non-commutative algebraic structures.

Abstract

Some Gr\"{u}ss type inequalities in semi-inner product modules over $C^*$-algebras and $H^*$-algebras for $n$-tuples of vectors are established. Also we give their natural applications for the approximation of the discrete Fourier and the Melin transforms in such modules.