Generalizations of Bohr's inequality in Hilbert $C^*$-modules

TL;DR

This paper introduces a new operator equality in Hilbert $C^*$-modules, leading to extended identities and generalized inequalities that build upon and expand previous work in the area.

Contribution

It presents a novel operator equality in Hilbert $C^*$-modules and extends classical inequalities and identities to this setting.

Findings

Derived a new operator equality in Hilbert $C^*$-modules.

Extended Euler--Lagrange identity to Hilbert bundles.

Generalized several operator Bohr's inequalities.

Abstract

We present a new operator equality in the framework of Hilbert $C^*$-modules. As a consequence, we get an extension of the Euler--Lagrange type identity in the setting of Hilbert bundles as well as several generalized operator Bohr's inequalities due to O. Hirzallah, W.-S. Cheung-J.E. Pecaric and F. Zhang.