MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Due to the negative answer to my last question I want to know if at least the following is true:

Let H be an infinite dimensional separable complex Hilbert space with $S^1$-action. Let $\text{Gl}_{S^1}(H)$ be the space of invertible, bounded and equivariant linear maps (from H to H).

Is $\text{Gl}_{S^1}(H)$ path-connected? If not, what is known about the components?

Of course, I would be happy enough if you point out references.

share|cite|improve this question
See the comment I just left on… – Alain Valette Oct 18 '11 at 12:11
Again, thank you. This helps me a lot. – J. Fabian Meier Oct 18 '11 at 13:38

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.