%0 Journal Article
%T A characterization of The operator-valued triangle equality
%A Tsuyoshi Ando
%A Tomohiro Hayashi
%J Mathematics
%D 2005
%I arXiv
%X We will show that for any two bounded linear operators $X,Y$ on a Hilbert space ${\frak H}$, if they satisfy the triangle equality $|X+Y|=|X|+|Y|$, there exists a partial isometry $U$ on ${\frak H}$ such that $X=U|X|$ and $Y=U|Y|$. This is a generalization of Thompson's theorem to the matrix case proved by using a trace.
%U http://arxiv.org/abs/math/0509539v1