Efficient Approaches for Verifying the Existence and Bound of Inverse of Linear Operators in Hilbert Spaces

This paper describes some numerical verification procedures to prove the invertibility of a linear operator in Hilbert spaces and to compute a bound on the norm of its inverse. These approaches improve on previous procedures that use an orthogonal projection of the Hilbert space and its a priori error estimations. Several verified examples which confirm the effectiveness of the new procedures are presented.