Hermitian moment sequences
are generalizations of classical power moment sequences to bounded operators on a
Hilbert space. The main result is that every indeterminate Hermitian moment
sequence on a complex Hilbert space can be imbedded in a determinate Hermitian
moment sequence on an enlarged Hilbert space in the sense that the first sequence
is a compression of the second. This implies the existence of determinate
Hermitian moment sequences which, when compressed, are indeterminate
and leads to the following questions: Which orthogonal projections on the
Hilbert space give rise to determinate compressions of a fixed, determinate
sequence? What structure do these projections induce on the underlying Hilbert
space?
