|Apr22-10, 02:41 PM||#1|
I am trying to find an example of a diagonal linear operator T in L(H) H is hilbert space that is bounded but not compact and also one which is compact but not Hilbert-Schmidt. any Ideas??
Where diagonal means Ten=§en where § is the eigenvalue and en is on orthonormal basis.
|Apr22-10, 03:50 PM||#2|
(Instead of diagonal, I would say diagonalizable, since it depends on the chosen basis so is not an intrinsic property of the operator.)
The identity operator I is diagonalizable (well, I is of course diagonal w.r.t. every basis), bounded, but not compact.
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