| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
The following are the main results of our project.(1) In the space of (possibly unbounded) self-adjoint operators, we determined exactly on which closed subsets of the real line the analogue of the Weyl-von Neuman theorme holds.
(2) We constructed a strongly unitarily representable Polish SIN group which is not of finite type (3) We constructed a one-parameter automorphism group of R_+ on the relative bicentralizer algebra defined for an inclusion of type III factors (the smaller one being of type III_1). We used showed that the properties of this flow are closely related to the structure of the underlying type III subfactors.(4) We studied global properties of the unitary groups of C* ana von Neumann algebras. In particular, we showed that there are many unital C* algebras A for which the identity component U_0(A) of its unitary group has property (FH) (any continuous affine isometric action on a real Hilbert space admits a fixed point) but fails to have property (T) of Kazhdan.
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