Unbounded operator algebras and the applications to the quantum physics

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We have studied unbounded Tomita-Takesaki theory which plays an important role for the structure theory and for applications to the quantum physics in the studies of algebras of unbounded operators (O^*-algebras, partial O^*-algebras). Weights on (partial) O^*-algebras are important for the physical applications (for example, the BCS-models) and for the structure of (partial) O^*-algebras.We have defined the notion of standard weights on (partial) O^*-algebras which is possible to develop the unbounded Tomita-Takesaki theory, and generalized the modular theory, Connes cocycle theorem and Randon-Nikodym theorem for von Neumann algebras to the case of (partial) O^*-algebras. We have tried to apply the existence of Haar measur in the locally compact quantum group.Furthermore, we have investigated weights and unbounded C^*-algebras for the structure theory and the representation theory of (locally convex) *-algebras.