Frames Generated by Subspace Addition

Abstract

Given two subspaces M and N of a Hilbert space, and frames associated with each of the subspace, the question addressed in this report is that of determining when the union of the two frames is a fame for the direct sum space M + N. We provide sufficient conditions for the union of the two frames to be a frame for, M + N and also estimates for the frame bounds. The results discussed here are given in terms of the relative geometry of subspaces. Some simple examples in which the frame bounds can be explicitly computed are provided to demonstrate accuracy of the frame bound estimates.