Vol. 66, No. 2, 1976

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ISSN: 0030-8730
An imbedding theorem for indeterminate Hermitian moment sequences

Francis Joseph Narcowich

Vol. 66 (1976), No. 2, 499–507

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?

Mathematical Subject Classification 2000
Primary: 47B99
Secondary: 44A50
Received: 2 April 1976
Published: 1 October 1976
Francis Joseph Narcowich