Perturbation Theorems for Frames and Riesz Bases

Abstract

This paper gives a perturbation theorem for frames in a Hilbert space which is a generalization of a result by Ping Zhao. It is proved that the condition a linear operator is invertible can be weakened to be surjective, and a similar result also be obtained for a Riesz basis. The perturbation theorems for frames and Riesz bases in a Hilbert space were studied by operator theory in functional analysis.