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Results tagged with perturbation-theory
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user 48839
3
votes
Accepted
Uniform decay of operator norm for smooth family of operators
This works, essentially because $\|T^k\|^{1/k}$ for a given $k=n$ also controls this quantity for $k\ge n$.
More specifically, suppose that $\|T^n\|^{1/n}\le 1-\delta$. Clearly, $\|T^{kn}\|^{1/kn}\le …
- 24.2k
1
vote
Lipschitz continuity of eigenprojections
I don't know about the fine details of the actual question, but can provide some (perhaps unhelpful) context: a related general notion is that of operator differentiable functions, defined as those $f …
- 24.2k
3
votes
Accepted
Gap-opening perturbations of the periodic Schrödinger operator
Here's a slightly different (direct) method that gives similar conclusions: Since we have a double periodic eigenvalue at $\widehat{E}$ (let me in fact assume that $\widehat{E}=0$, for convenience), t …
- 24.2k