3.5 Operator inverses
A linear mapping 
from a vector space 
into a vector space 
is one-to-one if 
and onto if 
. When 
is both one-to-one and onto it is said to be bijective. Bijective linear mappings are invertible. That is, there exists a linear mapping 
from 
to 
such that 
and 
are the identity transformation on their respective spaces.
Suppose now that and are Banach spaces and that is bijective. ...
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