Let H be a Hilbert space C. (a) State the uniform boundedness principle and the closed graph theorem. (b) A linear operator A: H→ H is called self-adjoint if Vz, y EH one has (Ax, y) = (1, Ay). (i) Use the uniform boundedness principle to show that any self-adjoint operator A is bounded. (ii) Use the closed graph theorem to show that any self-adjoint operator A is bounded.

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