
What this book is about: approximants.- Preliminaries.- Self-adjoint and positive approximants.- Commutator approximants.- Spectral, and numerical range, approximants.- Unitary, isometric and partially isometric approximation of positive operators.

This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants...