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Resolvent estimate of compact perturbation of self-adjoint operator
$begingroup$
Let $T$ be a selfadjoint operator on Hilbert space $H$. Then we know that there is a resolvent estimation $$leftlVert (lambda-T)^{-1}rightrVert = frac{1}{dist(lambda,sigma(T))}, lambda in rho(T).$$
But what if we want to consider the compact perturbation, that is, operator
$A = T+ D,$
where $D$ is a compact operator on $H$. Is there any known results on the resolvent estimate? Does anyone know some related references ? Thank you very much.
reference-request spectral-theory
asked Jan 8 at 4:20
BowenBowen
61
$endgroup$
add a comment |
$begingroup$
Let $T$ be a selfadjoint operator on Hilbert space $H$. Then we know that there is a resolvent estimation $$leftlVert (lambda-T)^{-1}rightrVert = frac{1}{dist(lambda,sigma(T))}, lambda in rho(T).$$
But what if we want to consider the compact perturbation, that is, operator
$A = T+ D,$
where $D$ is a compact operator on $H$. Is there any known results on the resolvent estimate? Does anyone know some related references ? Thank you very much.
reference-request spectral-theory
asked Jan 8 at 4:20
BowenBowen
61
$endgroup$
add a comment |
$begingroup$
Let $T$ be a selfadjoint operator on Hilbert space $H$. Then we know that there is a resolvent estimation $$leftlVert (lambda-T)^{-1}rightrVert = frac{1}{dist(lambda,sigma(T))}, lambda in rho(T).$$
But what if we want to consider the compact perturbation, that is, operator
$A = T+ D,$
where $D$ is a compact operator on $H$. Is there any known results on the resolvent estimate? Does anyone know some related references ? Thank you very much.
reference-request spectral-theory
asked Jan 8 at 4:20
BowenBowen
61
$endgroup$
Let $T$ be a selfadjoint operator on Hilbert space $H$. Then we know that there is a resolvent estimation $$leftlVert (lambda-T)^{-1}rightrVert = frac{1}{dist(lambda,sigma(T))}, lambda in rho(T).$$
But what if we want to consider the compact perturbation, that is, operator
$A = T+ D,$
where $D$ is a compact operator on $H$. Is there any known results on the resolvent estimate? Does anyone know some related references ? Thank you very much.
reference-request spectral-theory
reference-request spectral-theory
asked Jan 8 at 4:20
BowenBowen
61
asked Jan 8 at 4:20
BowenBowen
61
edited Jan 8 at 4:29
Bowen
asked Jan 8 at 4:20
BowenBowen
61
asked Jan 8 at 4:20
BowenBowen
61
asked Jan 8 at 4:20
BowenBowen
61
61
add a comment |
add a comment |
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