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Let and be operator spaces such that and are embedded in
a Hausdorff topological vector space.
is given a norm via
.
So we have:
.
The operator space is called the
intersection of and .
For operator spaces75 and , by embedding
in
we obtain an operator space structure
.
We write
.
The quotient operator space
is called the
sum of and and is denoted by .
We have
.
Footnotes
- ... spaces75
-
Let , be Banach spaces. Then we have their 1-direct sum
with the norm
and their sum with the quotient norm
Prof. Gerd Wittstock
2001-01-07