All Questions
Tagged with hilbert-spaces sp.spectral-theory
3 questions
6
votes
2
answers
539
views
Is there a reasonable notion of spectral theorem on a pre-Hilbert space?
I'm trying to understand how bad things could possibly get without Cauchy completeness as a criterion for Hilbert spaces in quantum mechanics. Obviously, doing calculus on a pre-Hilbert space would be ...
- 269
3
votes
1
answer
232
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what is about the corresponding power series?
According to the papers The absolutely continuous spectrum of Jacobi matrices and these lecture notes:
periodicity ~ potential well or lattice (order)
lack of absolutely continued spectrum ~ Anderson ...
- 3,094
0
votes
0
answers
68
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$H$ self-adjoint with mass gap, $P≥0,Ω∈D(P),H+λP$ self-adjoint $⟹$ for $λ$ small, $H+λP$ has gap?
Suppose $H$ is a self-adjoint operator on a Hilbert space having a simple isolated least eigenvalue $0$ with gap $1$ ( $H\Omega = 0$, $\Vert \Omega\Vert = 1$ ), $P$ is a non-negative symmetric ...
- 221