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Results tagged with operator-theory
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user 37366
Spectrum, resolvent, numerical range, functional calculus, operator semigroups. Special classes of operators: compact, Fredholm, dissipative, differential, integral, pseudodifferential, etc.
2
votes
0
answers
55
views
$\|(A_n-z)^{-1} - (A-z)^{-1}\|\to 0\;\Rightarrow\; \|e^{-tA_n}-e^{-tA}\|\to 0$ for general $...
In short, the question is whether norm-resolvent convergence implies operator-norm convergence of the assocoated semigroups. More specifically, assume the following:
The $A_n$ generate contraction se …
- 241
6
votes
1
answer
1k
views
Is the sum of spectral projections a projection?
Let $T$ be a closed operator on a Hilbert space with discrete spectrum. Then for $\{\lambda_1,...\lambda_n\}\in\sigma(T)$ one can define the spectral projections
$$P_{\{\lambda_1,...\lambda_n\}}=\frac …
- 241