Frame expansions in separable Banach spaces

• DOI: 10.1016/j.jmaa.2005.02.015
• Publication Date: 2005-03-18T14:42:40Z
• Authors: Pete Casazza; Ole Christensen; Diana T. Stoeva
• Keywords: Frames; Expansions in Banach spaces; Applied Mathematics; p-Frames; 0101 mathematics; 01 natural sciences; Analysis; Banach frames

AbstractBanach frames are defined by straightforward generalization of (Hilbert space) frames. We characterize Banach frames (and Xd-frames) in separable Banach spaces, and relate them to series expansions in Banach spaces. In particular, our results show that we can not expect Banach frames to share all the nice properties of frames in Hilbert spaces.