Next: Complete boundedness
Up: Completely bounded bilinear mappings
Previous: Amplification
  Contents
  Index
Jointly
complete boundedness
Let
be operator spaces.
A bilinear mapping
is called
jointly completely bounded
[BP91, Def. 5.3 (jointly completely bounded)]
if the norms of the
joint amplifications
of
are uniformly bounded:
where
,
,
[BP91, Def. 5.3].
The norm
equals the norm
of the linearization
on the projective operator space tensor product.
denotes the operator space consisting of the jointly completely bounded
bilinear maps.
One obtains a norm on each matrix level by the identification
We have
completely isometrically.
By taking the transposition
we obtain a
complete isometry
Prof. Gerd Wittstock
2001-01-07