Unbounded^*-representations and their applications of quantum physics

81. A. Inoue，S. J. Bhatt和M Fragoulopoulou研究了（局部凸）*-代数的良好表现。特别是，井上和Fragoulopoulou研究了行为良好的 * 表示（局部凸）*-代数。Inoue，S. Ota和H.Kurose将它们应用于量子群。Inoue，F.Bagarello，Fragoulopoulou，K. D. Kursten和C. Trapani研究了包含C*-代数A的局部凸 *-代数A[τ]的代数结构和表示.特别地，我们定义了局部凸拟C*-代数，它是C*-代数到局部凸拟 *-代数的推广，并对其结构和表示进行了研究。Inoue和Bhatt研究了C*-代数中的非交换微分结构。我们研究了由Blackadar和Cuntz引入的微分代数的谱不变性，C^∞-泛函演算。进一步研究了C*-代数和C*-结构中的光滑子代数. Inoue，H.Ogi和M.高仓健考虑了冯诺依曼代数的条件期望到O*-代数的条件期望的推广。定义并研究了O*-代数的弱条件期望和无界条件期望的概念。特别地，我们研究了在什么条件下无界条件期望是条件期望. Inoue，Bagarello，Trapani研究了O*-代数的完全正映射和O*-代数的导子。

81. A. Inoue, S.J. Bhatt and M Fragoulopoulou studied well-behaved representations of (locally convex) *-algebras. In particular, Inoue and Fragoulopoulou studied well-behaved *representations of (locally convex) *-algebras. Inoue, S. Ota and H.Kurose applied them to quantum groups.2. Inoue, F.Bagarello, Fragoulopoulou, K.D. Kursten and C. Trapani studied the algebraic structure and representation of locally convex *-algebra A[τ] containing C*-algebra A. In particular, we defined locally convex quasi C*-algebras which are a generalization of C*-algebras to locally convex quasi *-algebras, and proceeded the studies of their structures and representations.3. Inoue and Bhatt studied noncommutative differential structure in C*-algebras. We investigated the spectral invariance, the C^∞-functional calculus of differential algebras introduced by Blackadar and Cuntz. Furthermore, we studied smooth subalgebras in C*-algebras and C*-structure.4. Inoue, H.Ogi and M. Takakura considered a generalization of conditional expectations for von Neumann algebras to those for O*-algebras. We defined and investigated the notions of weak conditional expectations and unbounded conditional expectations of O*-algebras. In particular, we investigated under which conditions an unbounded conditional expectation is a conditional expectation.5. Inoue, Bagarello, Trapani studied completely positive maps of O*-algebras and derivations of O*-algebras.