Positive sesquilinear form measures and generalized eigenvalue expansions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:336

Article

Hytoenen, Tuomas ; Pellonpaeae, Juha-Pekka ; Ylinen, Kari

关键词: sesquilinear form;    normal operator;    generalized eigenvector;    naimark dilation;    direct integral;    (Semi)spectral measure;   

DOI  :  10.1016/j.jmaa.2007.03.051

来源: Elsevier

【 摘 要 】

Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered with the aim of providing a framework for their generalized eigenvalue type expansions. Though there are formal similarities with earlier approaches to special cases of the problem, the paper differs e.g. from standard rigged Hilbert space constructions and avoids the introduction of nuclear spaces. The techniques are predominantly measure theoretic and hence the Hilbert spaces involved are separable. The results range from a Naimark type dilation result to direct integral representations and a fairly concrete generalized eigenvalue expansion for unbounded normal operators. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free