Towards characterizations of approximate Schauder frame and its duals for Banach spaces

摘要

Characterizations for a frame and its duals are known for separable Hilbert spaces. In this paper, we characterize a class of approximate Schauder frame and its duals for separable Banach spaces. We also give an operator-theoretic characterization for similarity of ASFs. Our results encode the results of Holub, Li, Balan, Han, and Larson. We also address orthogonality of ASFs.