TITLE:
Stability of Operator-Valued Truncated Moment Problems
AUTHORS:
L. Lemnete-Ninulescu
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
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.4,
April
30,
2013
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.