A Recursive approach to the matrix moment problem

Abstract

In this paper, we study the truncated matrix moment problem in one variable through recursive matrix extensions. We give necessary and sufficient conditions for a recursive matrix extension of finite data to be a matrix moment sequence in the classical cases of Hamburger, Stieltjes, and Hausdorff moment problems. We also discuss matricial subnormal completion and matricial $k$--hyponormal completion problems and provide an analog of Stampfli's Theorem on flat propagation for $2$--hyponormal matricial weighted shifts.

arXiv comment27 pages