Diagonalization and representation results for nonpositive sesquilinear form measures

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:338

Article

Hytoenen, Tuomas³  Pellonpaeae, Juha-Pekka¹  Ylinen, Kari² 

[1] Univ Turku, Dept Phys, FI-20014 Turku, Finland

[2] Univ Turku, Dept Math, FI-20014 Turku, Finland

[3] Univ Helsinki, Dept Math & Stat, FI-00014 Helsinki, Finland

关键词: sesquilinear form;    operator measure;    bounded variation;    diagonalization;    Naimark dilation;    direct integral;   

DOI  :  10.1016/j.jmaa.2007.05.063

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free