Show that where is the spectrum of and is the space consisting of all linear operators mapping elements fromthe Hilbert space to itself here's an idea exists, and is the resolvant of is this on the right track?
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I would suggest you think of it this way: if , i.e., if , then there exists such that where (or ( , doesn't matter). That's just the definition of resolvent. Can you see how this translates to in terms of and ?
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