engleski

On the C*-valued triangle equality and inequality in Hilbert C*-modules

We prove that for two elements x, y in a Hilbert A-module V the triangle equality |x+y|=|x|+|y| holds if and only if the inner product of x and y is equal to |x||y|. In addition, we establish some kind of a C*-valued triangle inequality in a Hilbert C*-module over a unital C*-algebra.

C*-algebra ; Hilbert C*-module ; linking algebra ; C*-valued triangle (in)equality

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