A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Diagonalization and representation results for nonpositive sesquilinear form measures
Tekijät: Hytönen Tuomas, Pellonpää Juha-Pekka, Ylinen Kari
Kustantaja: Elsevier
Julkaisuvuosi: 2008
Lehti: Journal of Mathematical Analysis and Applications
Tietokannassa oleva lehden nimi: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Lehden akronyymi: J MATH ANAL APPL
Vuosikerta: 338
Numero: 1
Aloitussivu: 716
Lopetussivu: 725
Sivujen määrä: 10
ISSN: 0022-247X
eISSN: 1096-0813
DOI: https://doi.org/10.1016/j.jmaa.2007.05.063
Tiivistelmä
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.
Avainsanat:
bounded variation, diagonalization, direct integral, Naimark dilation, operator measure, sesquilinear form
Turun yliopiston Tutkimustietojärjestelmän portaali