Math 131

1) Let P=d/dx and Q=x (i.e. (Qf)(x)=x f(x)), be the momentum and position operators defined in L2(R). Compute their commutator. 2) Prove that the anti-derivative operator defined on C[a,b], is bounded with respect to the sup norm, and its norm is ||R||=(b-a). 3) Prove the Hahn-Banach Theorem. 4) Prove that a unitary operator is an isometry. ................
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