Some perturbation results for quasi-bases and other sequences of vectors

TL;DR

This paper explores how small changes affect sequences of vectors in Hilbert spaces, focusing on their reconstruction capabilities and extending results to distributional contexts.

Contribution

It provides new perturbation results for quasi-bases and vector sequences, including initial findings in distributional settings.

Findings

Perturbation results for sequences sharing reconstruction formulas

Extension of results to distributional frameworks

Preliminary insights into stability of vector sequences

Abstract

We discuss some perturbation results concerning certain pairs of sequences of vectors in a Hilbert space $\Hil$ and producing new sequences which share, with the original ones, { reconstruction formulas on a dense subspace of $\Hil$ or on the whole space}. We also propose some preliminary results on the same issue, but in a distributional settings.