Give one example of each of the following. Also justify your choice of

Question

Give one example of each of the following. Also justify your choice of example.

i) A self-adjoint operator on $l^2$ .

ii) A normal operator on a Hilbert space which is not unitary.

06 Feb 2024

Answer :

Word Count : 190

i) A self-adjoint operator on $ \ell^2 $: Let's consider the left shift operator $ L $ on $ \ell^2 $, defined by $ L(x_1, x_2, x_3, \ldots) = (x_2, x_3, x_4, \ldots) $. This operator is self-adjoint ______ _______ _______ _______ __________ __________ ____.
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