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.

• Periodical: Applied Mechanics and Materials (Volumes 433-435)
• Pages: 44-47
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.433-435.44
• Online since: October 2013
• Authors: Xue Mei Xiao
• Keywords: Frame, Linear Operator, Perturbation, Riesz Basis, Surjective

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