There's like three applications of the uniform boundedness principle in wikipedia:
1) If a sequence of bounded operators converges pointwise to an operator, then the limit operator is also bounded, and the convergence is uniform on compact sets.
2) Any weakly bounded subset of a normed space is bounded.
3) A result in pointwise convergence of Fourier series.
I am just asking if there's more interesting applications of the uniform boundedness principle.