### Abstract

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.

Original language | English |
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Number of pages | 22 |
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Publication status | Published - 1996 |

## Cite this

Christensen, O., & Casazza, P. (1996).

*Perturbation of Operators and Applications to Frame Theory*.