Geometric and operator measures of degeneracy for the set of solutions to the Stieltjes matrix moment problem

Abstract

The ranks of the limit Weyl intervals are known to serve as the geometric measure of degeneracy of the solution set to a Stieltjes matrix moment problem. This paper puts forward the first operator measure of degeneracy for the solution set to a Stieltjes matrix moment problem in terms of the deficiency vectors of a pair of associated positive symmetric operators. A relationship between the geometric and operator measures of degeneracy for a Stieltjes matrix moment problem is established, from which some corollaries about the Stieltjes matrix moment problem are obtained. Bibliography 19 titles.