The existence of unitary dilations makes it possible to study arbitrary
contractions on a Hilbert space using the tools of harmonic analysis.
The first edition of this book was an account of the progress done in
this direction in 1950-70. Since then, this work has influenced many
other areas of mathematics, most notably interpolation theory and
control theory. This second edition, in addition to revising and
amending the original text, focuses on further developments of the
theory, including the study of two operator classes: operators whose
powers do not converge strongly to zero, and operators whose functional
calculus (as introduced in Chapter III) is not injective. For both of
these classes, a wealth of material on structure, classification and
invariant subspaces is included in Chapters IX and X. Several chapters
conclude with a sketch of other developments related with (and
developing) the material of the first edition.