  This article, addressed to a general audience of functional analysts, is
intended to be an illustration of a few basic principles from `noncommutative
functional analysis', more specifically the new field of {\em operator spaces.}
In our illustration we show how the classical characterization of (possibly
non-surjective) isometries between function algebras generalizes to operator
algebras. We give some variants of this characterization, and a new proof which
has some advantages.
