Title: On the structure of Hausdorff moment sequences of complex matrices,
Abstract: The paper treats several aspects of the truncated matricial
$[\alpha,\beta]$-Hausdorff type moment problems. It is shown that each
$[\alpha,\beta]$-Hausdorff moment sequence has a particular intrinsic
structure. More precisely, each element of this sequence varies within a closed
bounded matricial interval. The case that the corresponding moment coincides
with one of the endpoints of the interval plays a particular important role.
This leads to distinguished molecular solutions of the truncated matricial
$[\alpha,\beta]$-Hausdorff moment problem, which satisfy some extremality
properties. The proofs are mainly of algebraic character. The use of the
parallel sum of matrices is an essential tool in the proofs.