Characterization of equality in a generalized Dunkl--Williams inequality

TL;DR

This paper generalizes the Dunkl--Williams inequality within Hilbert C*-modules, characterizes the equality case, and derives new and existing results in the field.

Contribution

It introduces a generalized inequality framework in Hilbert C*-modules and characterizes when equality holds, extending previous results.

Findings

Established a generalized Dunkl--Williams inequality in Hilbert C*-modules

Characterized the conditions for equality in the generalized inequality

Derived new and known results related to the inequality

Abstract

We establish a generalization of the Dunkl--Williams inequality and its inverse in the framework of Hilbert $C^*$-modules and characterize the equality case. As applications, we get some new results and some known results due to Pe\v{c}ari\'c and Raji\'c [Linear Algebra Appl. 425 (2007), no. 1, 16--25].