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The space
of
-tupels over an operator space
can be made into an operator
space for instance by reading the
-tupels as
- or as
-matrices. This leads to the frequently used
columns and
rows of an operator space
:

and

.
The first matrix level of these spaces are

and

, respectively.
If
, the spaces
and
are not completely isometric. In
general even the first matrix levels
and
are not isometric.
is called the
p-dimensional column space
and
the
p-dimensional row space.
The first matrix levels of
and
are isometric to
,
but
and
are not
completely isometric .
Prof. Gerd Wittstock
2001-01-07