Access the full text.
Sign up today, get DeepDyve free for 14 days.
(2018)
The strong Trotter property for locally μ-convex
A. Kriegl, P. Michor, A. Rainer (2015)
An exotic zoo of diffeomorphism groups on R n
大森 英樹 (1997)
Infinite-dimensional Lie groups
(1997)
The exponential map on D s µ
K. Neeb (2010)
On Differentiable Vectors for Representations of Infinite Dimensional Lie GroupsarXiv: Representation Theory
Helge Glockner (2015)
Measurable regularity properties of infinite-dimensional Lie groups
K. Neeb, Hadi Salmasian (2012)
Differentiable vectors and unitary representations of Fréchet–Lie supergroupsMathematische Zeitschrift, 275
K. Neeb (2006)
Towards a Lie theory of locally convex groupsJapanese Journal of Mathematics, 1
Y. Maeda, Hideki. Omori, Osamu Kobayashi, A. Yoshioka (1985)
On Regular Fréchet-Lie Groups VIII; Primordial Operators and Fourier Integral OperatorsTokyo Journal of Mathematics, 08
V. Arnold, B. Khesin (1998)
Topological methods in hydrodynamics
O. Bratteli (1979)
Operator Algebras And Quantum Statistical Mechanics
M. Gordina (2005)
Hilbert–Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometryJournal of Functional Analysis, 227
Martins Bruveris, Franccois-Xavier Vialard (2014)
On Completeness of Groups of DiffeomorphismsarXiv: Differential Geometry
In this paper we study the Lie theoretic properties of a class of topological groups which carry a Banach manifold structure but whose multiplication is not smooth. If G and N are Banach–Lie groups and π : G → Aut(N) is a homomorphism defining a continuous action of G on N, then H := N ⋊π G is a Banach manifold with a topological group structure for which the left multiplication maps are smooth, but the right multiplication maps need not be. We show that these groups share surprisingly many properties with Banach–Lie groups: (a) for every regulated function ξ : [0, 1] → 𝔥 the initial value problem γ ⋅ $$ \overset{\cdot }{\gamma } $$ (t) = γ(t)ξ(t), γ(0) = 1 H , has a solution and the corresponding evolution map from curves in 𝔥 to curves in H is continuous; (b) every C 1-curve γ with γ(0) = 1 and γ′(0) = x satisfies lim n→∞ γ(t/n) n = exp(tx); (c) the Trotter formula holds for C 1 one-parameter groups in H; (d) the subgroup N ∞ of elements with smooth G-orbit maps in N carries a natural Fréchet–Lie group structure for which the G-action is smooth; (e) the resulting Fréchet–Lie group H ∞ := N ∞ ⋊ G is also regular in the sense of (a).
Transformation Groups – Springer Journals
Published: May 29, 2018
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.