Diagonalization and representation results for nonpositive sesquilinear form measures

: Hytönen Tuomas, Pellonpää Juha-Pekka, Ylinen Kari

Publisher: Elsevier

: 2008

: Journal of Mathematical Analysis and Applications

: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

: J MATH ANAL APPL

: 338

: 1

: 716

: 725

: 10

: 0022-247X

: 1096-0813

DOI: https://doi.org/10.1016/j.jmaa.2007.05.063

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.