Algebraically we have
. If
is closed, then
together with the quotient norm on each matrix level is matricially normed
(an operator space if
is one). The quotient mapping
is a
complete quotient mapping.
More generally, a
subspace of a matricially normed space (operator
space) is a matricially normed space (operator space)
together with a
completely isometric operator
. A
quotient of
is a matricially normed space
(operator space)
together with a complete quotient mapping
.