MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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

It is known that an intertwining (or even approximately intertwining) diagram implies the isomorphism of the limit algebras. Under what conditions the converse holds?

share|cite|improve this question
up vote 6 down vote accepted

The converse holds if the inductive limits involve semiprojective building blocks. That is: suppose $$\varinjlim (A_i,\phi_i^{i'}) \cong \varinjlim (B_j,\psi_j^{j'})$$ (here my notation is $\phi_i^{i'}:A_i \to A_{i'}$, etc.), and each $A_i$ and $B_j$ are separable and semiprojective, then there exists subsequences $(A_{i_k}), (B_{j_k})$ and an approximate intertwining between these.

share|cite|improve this answer
    
Thank you very much. – David May 10 '13 at 18:19

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.