Modifying a resolution of the identity by the action of a linear operator

Abstract

The main purpose of this paper is to investigate the behavior of the Hilbert space valued functions ϕ that are obtained by applying a linear operator W to a resolution of the identity (i.e. a continuous Parseval frame) ζ. After reviewing the case when W is bounded with bounded inverse, we study, in more detail, generalized Riesz maps, i.e. the image of a ζ by an invertible closed linear operator W.