A celebrated classical result states that an operator Uon a Banach space is invertible, if it is close enough to the identityoperator I. Here we showthat U actually is invertible under a much weaker condition. As anapplication we prove new theorems concerning stability of frames (andframe-like decompositions) under perturbation in both Hilbert spacesand Banach spaces.
|Number of pages||22|
|Publication status||Published - 1996|