Perturbation for Frames for a Subspace of a Hilbert Space

Ole Christensen, C. deFlicht, C. Lennard

Research output: Book/ReportReportResearchpeer-review

Abstract

We extend a classical result stating that a sufficiently small perturbation$\{ g_i \}$ of a Riesz sequence $\{ f_i \}$ in a Hilbert space $H$ is again a Riesz sequence. It turns out that the analog result for a frame does not holdunless the frame is complete. However, we are able to prove a very similarresult for frames in the case where the gap between the subspaces$\overline{span} \{f_i \}$ and $\overline{span} \{ g_i \}$ is small enough. We give a geometric interpretation of the result.
Original language English
Number of pages 18 Published - 1997