Operators and frames (Q2857165)

In the setting of finite-dimensional Hilbert spaces, this work presents characterization results for operators which generate frames with a prescribed frame operator, operators which change the norm of the frame vectors by a constant multiple, and operators which generate equal norm Parseval frames. The article is organized as follows: The Introduction gives the basic definitions and the relevamce of the problems. In Section 1 the authors classify those operators which leave the frame operator invariant. A characterization of operators mapping frames to frames with comparable norms is provided in Section 2. Section 3 is then devoted to the study of operators which generate nearly Parseval frames. The question dealt with in this section is closely related to the Paulsen problem, which is still open, and the authors anticipate that their results will provide a new direction of attack.