The Banach adjoint 
of a bounded operator 
between Banach spaces
is defined by
 |
for every continuous linear functional 
and every 
. Thus the Banach adjoint reverses the direction of the
original operator and acts between the dual spaces.
For a densely defined linear operator 
, the domain
of 
consists of the 
for which 
extends to a continuous linear
functional on 
.
The density of 
makes this extension unique, and 
is this extension.
