A1 Refereed original research article in a scientific journal
Diagonalization and representation results for nonpositive sesquilinear form measures
Authors: Hytönen Tuomas, Pellonpää Juha-Pekka, Ylinen Kari
Publisher: Elsevier
Publication year: 2008
Journal: Journal of Mathematical Analysis and Applications
Journal name in source: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Journal acronym: J MATH ANAL APPL
Volume: 338
Issue: 1
First page : 716
Last page: 725
Number of pages: 10
ISSN: 0022-247X
eISSN: 1096-0813
DOI: https://doi.org/10.1016/j.jmaa.2007.05.063(external)
Abstract
We study decompositions of operator measures and more general sesquilinear form measures E into linear combinations of positive parts, and their diagonal vector expansions. The underlying philosophy is to represent E as a trace class valued measure of bounded variation on a new Hilbert space related to E. The choice of the auxiliary Hilbert space fixes a unique decomposition with certain properties, but this choice itself is not canonical. We present relations to Naimark type dilations and direct integrals. (C) 2007 Elsevier Inc. All rights reserved.
We study decompositions of operator measures and more general sesquilinear form measures E into linear combinations of positive parts, and their diagonal vector expansions. The underlying philosophy is to represent E as a trace class valued measure of bounded variation on a new Hilbert space related to E. The choice of the auxiliary Hilbert space fixes a unique decomposition with certain properties, but this choice itself is not canonical. We present relations to Naimark type dilations and direct integrals. (C) 2007 Elsevier Inc. All rights reserved.
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