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For a commutative
-algebra
, each bounded linear mapping
is automatically completely bounded with
[Loe75].16
Each normed space
is isometric to a
subspace of the commutative
-algebra
. Thus the operator space
is given as a subspace of
.
For
we have

.
The unit ball of
is given as the absolute matrix polar of
.
Footnotes
- ...Loebl75.16
- I. e.
is a
-space.
Prof. Gerd Wittstock
2001-01-07