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.

Number of pages | 18 |
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Publication status | Published - 1997 |
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