A Recursive approach to the matrix moment problem

TL;DR

This paper investigates the truncated matrix moment problem using recursive matrix extensions, providing conditions for sequences to be valid moment sequences and exploring related completion problems and properties.

Contribution

It introduces necessary and sufficient conditions for recursive matrix extensions to solve classical matrix moment problems and discusses related completion and hyponormality issues.

Findings

Established conditions for recursive matrix extensions to be moment sequences.

Analyzed matricial subnormal and hyponormal completion problems.

Extended Stampfli's flat propagation theorem to 2-hyponormal matricial weighted shifts.

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.