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 .