Linear operators on function spaces and geometric topology
Description: We characterized some isometries on the continuously differentiable function spaces over compact Riemannian manifolds as generalized weighted composition operators, and illustrated deformations of the isometry groups under norm-perturbations with some concrete manifolds. Some Banach-Stone type theorems were obtained in joint works with S.Oi, H.Koshimizu, O. Hatori and T.Miura. Also we showed that the topological Hochschild cohomology of Lipschitz algebras over compact geodesic spaces is infinite dimensional, which shows a contrast to the fact that global homological dimension of the smooth function algebra over a compact smooth manifold is equal to the dimension of the manifold.We studied the mean dimension of the shift maps on generalized inverse limits and obtained an estimate in terms of the lengths of periodic blocks. The result was applied to refine the dichotomy on the topological entropy of the shift map discovered by Erceg-Kennedy.
Amount: ¥4,550,000
Funding type: research
Funder scheme: Grant-in-Aid for Scientific Research (C)
Start date: 2017-04-01
End date: 2021-03-31
Investigator: Kazuhiro Kawamura
Institution: University of Tsukuba
Funded outputs count: 20
Funder award ID: 17K05241
OpenAlex ID: G601211971