Pisier introduced the analogous construction for operator spaces
[Pis96, §2]:
Let
be operator spaces
continuously embedded
in a Hausdorff topological vector space
.
Then we have specific norms on
and continuous linear
inclusions
for all
.76 The
interpolated operator space
is defined via
.
Let be an operator space,
a Hilbert space and
a bounded linear and injective
mapping with dense range
such that the mapping77
also is bounded, linear
and injective with dense range.
Then we have completely isometrically [Pis96, Cor. 2.4]: