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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- Feb 26th 2010, 01:23 PMMauritzvdwormspectrum of adjoint operator
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? - Feb 26th 2010, 03:38 PMNyrox
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 ?