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For a index set
,
.
is an operator space as
dual of the commutative
-algebra
, and each bounded
linear mapping
is automatically completely bounded with
.17
Each Banach space18
is isometric to a quotient of
. Thus the operator space
is given as a quotient of
.
For
we have

.
The unit ball of
is given as the absolute matrix bipolar of
.
Footnotes
- ....17
- I. e.
is a
-space.
- ... space18
-
A similar construction is possible for normed spaces.
Prof. Gerd Wittstock
2001-01-07