Next: -direct sums
Up: Direct sums
Previous: -direct sums
  Contents
  Index
Let be an index set and for each an operator space. Then there are an
operator space and complete contractions
with the following
universal mapping property: For each family of complete contractions
there is exactly one complete contraction
such that
for all .
is called -direct sum of the and is denoted by
.The are completely isometric.
One can construct a -direct sum for instance as the closure of the sums of the
images of the mappings
, where is the projection from
onto .
The equation
holds isometrically.
Prof. Gerd Wittstock
2001-01-07