Bessel type inequalities in Hilbert C*-modules

TL;DR

This paper extends classical Bessel inequalities to the setting of Hilbert C*-modules, providing new versions and generalizations of these inequalities within this broader mathematical framework.

Contribution

It introduces a novel version of the Bessel inequality and its generalizations specifically tailored for Hilbert C*-modules, expanding the scope of these inequalities.

Findings

Established a new Bessel inequality in Hilbert C*-modules

Generalized existing inequalities to the C*-module context

Enhanced understanding of inequalities in operator algebra frameworks

Abstract

Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombiari and Boas--Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert $C^*$-modules.