(Georgia Institute of Technology, 1994-06)
Christensen, Ole; Heil, Christopher E.; Georgia Institute of Technology. School of Mathematics; Universität für Bodenkultur. Institut für Mathematik
Banach frames and atomic decompositions are sequences which have basis-like properties
but which need not be bases. In particular, they allow elements of a Banach space to be written as combinations of the frame or atomic decomposition elements in a stable manner. However, these representations
need not be unique. Such exibility is important in many applications. In this paper, we prove that
frames and atomic decompositions in Banach spaces are stable under small perturbations. Our results are
strongly related to classic results on perturbations of Paley/Wiener and Kato. We also consider duality
properties for atomic decompositions, and discuss the consequences for Hilbert frames.