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Can anyone give me an example of such an operator (preferably, but not necessary, self-adjoint) on a Hilbert space? Not the usual ones you would find in a textbook (multiplication, integral, shift, etc etc etc).

I'd would like to calculate the norm and spectrum of it. Also, ones that aren't on doubly infinite sequence spaces (like discrete Laplace operator) would be good.

Thank you.

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up vote 3 down vote accepted

How about the Toeplitz operators on the Hardy-Hilbert space? ($H^2$ on the unit disk).

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Thanks. On first glance they look a bit too complex for me, but I'll have a closer look. –  A.A Apr 17 '11 at 22:28

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