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The C*-valued norm is defined on a Hilbert C*-module by its standard inner product. In this short note, we will prove that |x+y| ≤ |x|+|y| holds for all x, y ∈ E which is a Hilbert (script capital A sign)-module if and only if (script capital J sign)= <E,E>, the closed two-sided ideal in (script capital A sign), is a commutative C*-algebra. © ELEMEN.

A note on the triangle inequality for the C^✻-valued norm on a Hilbert C^✻-module