IMBEDDING THEOREM FOR INDETERMINATE HERMITIAN MOMENT SEQUENCES

Hermitian moment sequences are generalizations of classical power moment sequences to bounded operators on a Hubert space. The main result is that every indeterminate Hermitian moment sequence on a complex Hubert space can be imbedded in a determinate Hermitian moment sequence on an enlarged Hubert 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 Hubert space give rise to determinate compressions of a fixed, determinate sequence? What structure do these projections induce on the underlying Hubert space?. 1976, University of California, Berkeley. All Rights Reserved.

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