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An old man in the sea.
An old man in the sea.
09:40
Hi, could someone help me with this question of mine? math.stackexchange.com/questions/3431465/…
Martin Sleziak
Martin Sleziak
To make this a bit easier for others - the above message probably intended to link to: Why is $f(T)x=\frac{1}{2\pi i}\oint f(z)(z-T)^{-1}x \ dz$?
0
Q: Why is $f(T)x=\frac{1}{2\pi i}\oint f(z)(z-T)^{-1}x \ dz$?

An old man in the sea.Let $T$ be an element of $B(X)$, $f$ be analytic in a neighbourhood of the $T$'s spectrum. Why do we have the following $$f(T)x=\frac{1}{2\pi i}\oint f(z)(z-T)^{-1}x \ dz \text{ ?}$$ I would think we could only say that $f(T)x=\frac{1}{2\pi i}\oint f(z)(z-T)^{-1} \ dz\ x$. Is it because we kn...

functional-analysis functional-calculus
(I guess it's a bit more readable in this way - without having to click on the link. And it is probably better to link directly to the question than to a comment under the question.)
An old man in the sea.
An old man in the sea.
thanks ;) how did you do that?

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