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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