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Representation
Completely
bounded bilinear forms were first studied on C-algebras
,
[EK87].
For a bilinear form
the following properties are equivalent:
- (1)
- is completely bounded.
- (2)
- There is a constant such that
for all
, , .
- (3)
- There is a constant and states
,
such that
for all , .
- (4)
- There exist -representations
and
with cyclic vectors
,
and an operator
such that
for all , .
One can choose
and
.52
Footnotes
- ....52
- For further references see
[CS89, Sec. 4].
Prof. Gerd Wittstock
2001-01-07