Shorted operators and the structure of operators with numerical radius one (Q1105821)

The short of a positive operator A to a subspace S of the underlying Hilbert space is the maximum of those operators D satisfying \(0\leq D\leq A\) and range \(D\subseteq S\). The author uses this concept to prove that if the numerical radius of an operator T does not exceed 1, then \(T=2(1- C\) \(*C)^{1/2}C\) for some contraction C. In contrast to \textit{T. Ando}'s original proof [Acta Sci. Math. 34, 11-15 (1973; Zbl 0258.47001)], the present argument does not depend on knowing that T has a unitary 2- dilation.