PERTURBATIONS OF INVERTIBLE OPERATORS an‎d RIGHT INVERTIBLE OPERATORS

In this paper we prove several functional analytic prop- erties of these decompositions, and show how these properties ap- ply to Gabor and wavelet systems. A celebrated classical result states that an operator U on a Banach space is invertible if it is close enough to the identity operator 1 in the sense that j1 Uj < 1. Here we show that U actually is invertible under a much weaker condition