AM  Vol.3 No.12 , December 2012
Positive-Definite Operator-Valued Kernels and Integral Representations
Abstract: A truncated trigonometric, operator-valued moment problem in section 3 of this note is solved. Let be a finite sequence of bounded operators, with arbitrary, acting on a finite dimensional Hilbert space H. A necessary and sufficient condition on the positivity of an operator kernel for the existence of an atomic, positive, operator-valued measure , with the property that for every with , the moment of coincides with the term of the sequence, is given. The connection between some positive definite operator-valued kernels and the Riesz-Herglotz integral representation of the analytic on the unit disc, operator-valued functions with positive real part in the class of operators in Section 4 of the note is studied.
Cite this paper: L. Lemnete-Ninulescu, "Positive-Definite Operator-Valued Kernels and Integral Representations," Applied Mathematics, Vol. 3 No. 12, 2012, pp. 1990-1999. doi: 10.4236/am.2012.312274.

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