A Banach quotient space 
is the quotient vector
space of a Banach space 
by a closed linear subspace 
, equipped with
 |
Closedness makes this a norm, and completeness of 
implies completeness
of the quotient. The canonical map from 
to 
is bounded, linear,
and surjective. Conversely, a bounded linear surjection
between Banach spaces identifies the target, up to
linear isomorphism, with the quotient by its kernel.
The separable quotient problem asks
for an infinite-dimensional separable quotient of each infinite-dimensional Banach space.
