Suppose that A is a linear map from a Hilbert space H into itself that satisfies $\langle x,Ay\rangle=\langle Ax,y\rangle$ for all $x, y$ in $H$ . Show that A is bounded.
Please Give me hints to solve the problem.
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Hint: Try to use Banach-Steinhaus theorem – Simon Mar 28 '16 at 02:31
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http://math.stackexchange.com/questions/180495/hellinger-toeplitz-theorem-use-principle-of-uniform-boundedness – Simon Mar 28 '16 at 02:34