Stability of Operator-Valued Truncated Moment Problems

L. Lemnete-Ninulescu

Department of Mathematics, Politechnica University of Bucharest, Bucharest, Romania.

DOI: 10.4236/am.2013.44100                

Abstract

In this note a multidimensional Hausdorff truncated operator-valued moment problem, from the point of view of “stability concept” of the number of atoms of the obtained atomic, operator-valued representing measure for the terms of a finite, positively define kernel of operators, is studied. The notion of “stability of the dimension” in truncated, scalar moment problems was introduced in [1]. In this note, the concept of “stability” of the algebraic dimension of the obtained Hilbert space from the space of the polynomials of finite, total degree with respect to the null subspace of a unital square positive functional, in [1], is adapted to the concept of stability of the algebraic dimension of the Hilbert space obtained as the separated space of some space of vectorial functions with respect to the null subspace of a hermitian square positive functional attached to a positive definite kernel of operators. In connection with the stability of the dimension of such obtained Hilbert space, a Hausdorff truncated operator-valued moment problem and the stability of the number of atoms of the representing measure for the terms of the given operator kernel, in this note, is studied.

Keywords

Operator-Valued Positive-Definite Function; Unitary-Operator; Selfadjoint Operator; Joint Spectral Measure of a Commuting Tuple of Operators; Atomic Measure; Extension of Some Hermitian; Square; Positive Functional

Conflicts of Interest

The authors declare no conflicts of interest.

References

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