# Operator on Hilbert space

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• April 26th 2010, 11:01 AM
veljko
Operator on Hilbert space
$(H, \langle .,. \rangle)$ Hilbert space, and $f_1$, $f_2$ $\in H$.
Prove: $Af= \langle f,f_1 \rangle f_1 + \langle f,f_2 \rangle f_2$ is bounded linear operator, and calculate his norm.

...Idea: $|Af| \leq ||f|| ||f_1|| ||f_1|| + ||f|| ||f_2|| ||f_2||$ (??)