Projection Method for Frame Operator of Frame ofSubspaces

摘要

A frame of subspaces allows every element in a Hilbert space H to be writtenas a linear combination of the projection on subspaces, with coefficients called frameof subspaces coefficients. In practice it can be very difficult (sometimes impossible) toapply the frame of subspaces decomposition directly: the reason is that H usually is aninfinite-dimensional Hilbert space which makes it hard to invert the frame of subspacesoperator and so is frame of subspaces coefficients. In case that we can not find theSu;,, explicitly, we need to approximate it. In this paper, we introduce a method forapproximation of frame of subspaces operator.