On the <Emphasis Type="Italic">C</Emphasis>*-valued triangle equality and inequality in Hilbert <Emphasis Type="Italic">C</Emphasis>*-modules |
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| Authors: | Lj Arambašić R Rajić |
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| Institution: | (1) Department of Mathematics, University of Zagreb, Bijenička c. 30, 10000 Zagreb, Croatia;(2) Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia |
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| Abstract: | We prove that for two elements x, y in a Hilbert C*-module V over a C*-algebra  the C*-valued triangle equality |x + y| = |x| + |y| holds if and only if 〈x, y〉 = |x| |y|. In addition, if  has a unit e, then for every x, y ∊ V and every ɛ > 0 there are contractions u, υ ∊  such that |x + y| ≦ u|x|u* + υ|y|υ* + ɛe.
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| Keywords: | and phrases" target="_blank"> and phrases C*-algebra Hilbert C*-module linking algebra C*-valued triangle (in)equality |
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