Vol. 66, No. 2, 1976

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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