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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