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

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Abstract

We prove that for two elements x, y in a Hilbert C*-module V over a C*-algebra \( \mathcal{A} \) the C*-valued triangle equality |x + y| = |x| + |y| holds if and only if 〈x, y〉 = |x| |y|. In addition, if \( \mathcal{A} \) has a unit e, then for every x, y ∊ V and every ɛ > 0 there are contractions u, υ ∊ \( \mathcal{A} \) such that |x + y| ≦ u|x|u* + υ|y|υ* + ɛe.

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Authors and Affiliations

  1. Department of Mathematics, University of Zagreb, Bijenička c. 30, 10000, Zagreb, Croatia

    Lj. Arambašić

  2. Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Pierottijeva 6, 10000, Zagreb, Croatia

    R. Rajić

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  1. Lj. Arambašić
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  2. R. Rajić
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Correspondence to Lj. Arambašić.

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Arambašić, L., Rajić, R. On the C*-valued triangle equality and inequality in Hilbert C*-modules. Acta Math Hung 119, 373–380 (2008). https://doi.org/10.1007/s10474-007-7055-9

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  • DOI: https://doi.org/10.1007/s10474-007-7055-9

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