非正半双线性型测度的对角化和表示结果
Diagonalization and representation results for nonpositive sesquilinear form measures
摘要：
研究算子测度和更一般的半双线性型测度$E$分解为正部分的线性组合及其对角向量展开。其基本思想是将$E$表示为与$E$相关的新希尔伯特空间上的有界变差的迹族值测度。辅助希尔伯特空间的选择固定了具有某些性质的唯一分解，但这种选择本身不是规范的。我们目前的关系Naimark型膨胀和直接积分。
英文摘要：
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.
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