| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
|---|
| Outline of Final Research Achievements |
We show how to construct irreducible representations of the Banach *-algebra associated with a dynamical system in general, which consists of two major
procedures including what we call ergodic extension. An ergodic extension of a ergodic transformation on a (quasi-invariant) non-atomic probability measure space is an extension of the given one to an ergodic transformation of the system obtained by tensoring with a Type I factor. It is not clear this is at all possible. We were unable to prove this in general but show this is possible by two examples in the finite type I case, Bernoulli shifts and irrational rotations, whose proof depends on detailed property of these transformations.
|
