A1 Refereed original research article in a scientific journal
Positive sesquilinear form measures and generalized eigenvalue expansions
Authors: Hytonen T, Pellonpaa JP, Ylinen K
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Publication year: 2007
Journal:Journal of Mathematical Analysis and Applications
Journal name in sourceJOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Journal acronym: J MATH ANAL APPL
Volume: 336
Issue: 2
First page : 1287
Last page: 1304
Number of pages: 18
ISSN: 0022-247X
DOI: https://doi.org/10.1016/j.jmaa.2007.03.051
Abstract
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.
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.
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