Unbounded *-representations of partial *-algebras

从纯数学情形和物理应用两个方面研究了Hilbert空间中可闭算子的*-代数(O^*-代数)。关于O^*-代数理论的综述可以在K.Schudgen的专著《无界算子代数与表示论，算子理论：进展与应用第37卷，Birkhauser(1990)》和A.Inoue的讲座讲稿《无界算子代数中的Tomita-Takasaki理论，数学讲义，1699，Springer(1995)》中找到。此外，对可闭算子的部分*-代数(部分O^*-代数)从数学情形和物理应用方面进行了研究，但系统的研究似乎还不够。为了继续研究部分*-代数的*-表示，我们研究了下列内容：(1)在(部分)*-代数的无界*-表示中什么是好的*-表示？(2)系统地研究了部分O^*-代数的权重。(3)(1)和(2)在量子物理中的应用。因此，我们(A.Inoue，J.P.Antoine和C.TRapani)从Kluwer学术出版社出版了一本书《Partial*-Argebras及其算子实现，数学及其应用》，第553卷。

*-algebras (O^*-algebras) of closable operators in Hilbert space have been studied from the pure mathematical situation and the physical applications. A survey of the theory of O^*-algebras may be found in the monograph of K. Schmudgen "Unbounded Operator Algebras and Representation Theory, Operator Theory: Advances and Applications vol. 37, Birkhauser(1990)" and the lecture note of A. Inoue "Tomita-Takasaki Theory in Algebras of Unbounded Operator Algebras, Lecture Notes in Mathematics, 1699, Springer(1995)".Furthermore, partial *-algebras (partial O^*-algebras) of closable operators have been studied from the mathematical situations and the physical applications, but it seems that the systematic studies are insufficient. In order to proceed the studies of *-representations of partial *-algebras, we have investigated the following.(1) What is a well-behaved *-representation in unbounded *-representations of (partial) *-algebras?(2) Systemic studies of weights of partial O^*-algebras.(3) Applications of (1) and (2) to quantum physics.Thus we (A. Inoue, J. P. Antoine and C. Trapani) have published a book "Partial *-algebras and Their Operator Realizations, Mathematics and Its Applications vol. 553" from Kluwer Academic Publishers.