On the Davis-Kahan-Weinberger solution of the norm-preserving dilation problem (Q1058571)

This recently published solution of a problem which has found application in several different areas represents a major contribution to the dilation theory of contractions in Hilbert spaces. For finite-dimensional dilations, which is the case in typical applications to numerical analysis, the general solution can be reduced to pure matrix results. Our main purpose here is to present a simplified approach to this particularly significant case, by relying on some basic tools of matrix theory.