- #1

alle.fabbri

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I hope this is the right section to post such a question...

I'm studying the theory of resolvent from the QM books by A. Messiah and I read in a footnote (page 713) that the norm of the resolvent satisfies

[tex]

\|R_A(z)\| = \lVert \frac{1}{A-zI} \rVert \ge \text{dist}(z,\sigma(A))^{-1}

[/tex]

where the equality holds for self-adjoint operators and "dist" is the distance of z from the closest eigenvalue of A. Any idea of how to prove this? Links are good as well as answers...

Thanks to anyone who will answer...