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The definition of the
completely bounded
bilinear maps as well as the
Haagerup tensor product
relies on the
tensor
matrix multiplication
[Eff87]
of operator matrices
,
.
The
amplification
of the bilinear mapping
is given by
For scalar matrices
,
we have
We use the short hand notation
.
For linear maps
we denote by
the mapping
We then have
for
,
.
Let
be an
operator space tensor product .
We define the
tensor matrix multiplication
of operator matrices
,
of completely bounded maps by setting
Next: Interpolation
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Prof. Gerd Wittstock
2001-01-07