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 complete quotient mappings.
One can construct a -direct sum for instance as the linear subspace
of the
cartesian product of the , the being the projections on the
components. We have
,
and the operator space norm is given by
.
Prof. Gerd Wittstock
2001-01-07