a) is injective.
b) For each complete isometry
there is a complete contraction
such that
. I. e.
is completely contractively projectable
in each space containing it as a subspace.
c) For each complete isometry
and each complete contraction
there is a complete contraction
such that
. I. e. Complete contractions from
can be extended
completely
contractively to any space conaining
as a subspace.19
d) is completely isometric to a completely contractively projectable subspace of
for some Hilbert space
.
e) is completely isometric to
, where
is an injective
-algebra
and
and
are projections in
.
Robertson characterized the infinite dimensional injective subspaces
of up to isometry (not
complete isometry!). They are
,
,
,
and
. (Countable
-direct sums of such are again
comletely isometric to one of these.) If an injective subspace of
is isometric
to
, it is completely isometric to
or
.