Mathematics – Functional Analysis
Scientific paper
2007-06-14
J. Math. Anal. Appl. 338 (2008) 716-725
Mathematics
Functional Analysis
J. Math. Anal. Appl., in press
Scientific paper
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.
Hytonen Tuomas
Pellonpaa Juha-Pekka
Ylinen Kari
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