Fredholm frames for a Hilbert space H are introduced, which are special frames between frames and Riesz bases. By using operator theory method, some important properties and equivalent characterizations of Fredholm frames are obtained. It is proved that the set of all Fredholm frames for a Hilbert space H is an open set in the Banach space consisting of all Bessel sequences in H. It is proved that Fredholm frames are stable under small and operator perturbations. Inflations of frames and Riesz bases are also discussed.

frame; Fredholm frame; perturbation; Fredholm operator