invertible elements in a Banach algebra form an open set
Theorem - Let be a Banach algebra with identity element and be the set of invertible elements in . Let denote the open ball of radius centered in .
Then, for all we have that
and therefore is open in .
Proof : Let and . We have that
As is a group we must have .
So and the theorem follows.
|Title||invertible elements in a Banach algebra form an open set|
|Date of creation||2013-03-22 17:23:22|
|Last modified on||2013-03-22 17:23:22|
|Last modified by||asteroid (17536)|