These should be quite fundamental questions about the definitions about Hilbert manifold yet I cannot find answers about them after a long-time search:
- How is the tangent space at a point on a Hilbert manifold defined?
- What does it mean by a map between two Hilbert manifold being $C^k$ (I am particularly interested in $C^\infty$)?
- How is the differential of a map between two Hilbert manifold defined?
Thank you for helping me out!