engleski

The Dunkl-Williams equality in pre-Hilbert C*-modules

We give a necessary and sufficient condition for the norm equality ||x+y||=||x||+||y|| of elements x and y of a pre-Hilbert C*-module in terms of the numerical range. We use this result to characterize the equality attainedness in some generalizations of the Dunkl-Williams inequality in pre-Hilbert C*-modules.

triangle inequality; Dunkl-Williams inequality; numerical range

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