Positive-Definite Operator-Valued Kernels and Integral Representations

• 作者: L. Lemnete-Ninulescu
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Unitary-Operator SELF-ADJOINT OPERATOR Joint SPECTRAL Measure of a COMMUTING TUPLE of Operators SPECTRAL PROJECTOR Complex Moments Analytic Vectorial Functions
• 年，卷（期）: 2012,（12）
• 页码范围: 1990-1999
• 页数: 10页
• 分类号: O1

摘要

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.