arXiv subjects

Tsuyoshi Ando

Publications and source records attributed to Tsuyoshi Ando.

2 recordsLinked to original sources

arXiv2014

Operator log-convex functions and operator means

We study operator log-convex functions on $(0,\infty)$, and prove that a continuous nonnegative function on $(0,\infty)$ is operator log-convex if and only if it is operator monotone decreasing. Several equivalent conditions related to operator means are given for such functions. Operator log-concave functions are also discussed.

math.FA↗

arXiv2005

A characterization of The operator-valued triangle equality

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.

math.OA↗