Characterization of equality in a generalized Dunkl--Williams inequality

Abstract

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

11 pages, appeared in J. Math Anal. Appl. (Elsevier)