Do exercises 2.1.4, 2.1.5, 2.1.7, 2.1.12, 2.2.3, 2.3.2, 2.4.1, 3.1.6, 3.1.12, 3.1.15, 4.10.18 Also: Find an $L^\infty$ function on $\mathbb T$ whose Fourier series does not converge strongly. Show that the range projection of a self-adjoint operator is in the strong closure of the algebra generated by that operator. (Use books if necessary.)